Constants in a Triangle: Orthocenter and Circumcenter Relations
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Besondere Punkte/Special Points
This GeoGebra example demonstrates the geometric relationships between the orthocenter (H), circumcenter (O), and specially constructed points on the sides of triangle ABC. When three triangles A′BC, AB′C, and ABC′ are constructed on the sides, interesting constants and relationships emerge involving the triangle centers. Key mathematical concepts include orthocenter, circumcenter, centroid, similar triangles, angle bisectors, and geometric transformations. Construction uses commands: TriangleCenter for triangle centers, Line/Segment/Polygon for drawing, AngularBisector for angle bisectors, Mirror for reflections, and Intersect for finding intersections. Ideal for high school geometry teachers and students preparing for math competitions, helping deepen understanding of triangle center properties.
GeoGebra Commands & Parameters
TriangleCenter(A, B, C, 4) → UTriangleCenter(A, B, C, 3) → VLine(U, V) → m_1Segment(A, B) → a_1Segment(B, C) → b_1Segment(C, A) → c_1Polygon(B, A, n) → poly1, f, t_1, q_{16}, a_{154}, b_{154}, c_{154}, d_{154}, e_{154}, f_{155}, g_{155}, h_{155}, i_{155}, j_{155}, r_{16}, k_{155}, l_{155}, m_{155}, n_{155}, p_{155}, q_{155}, r_{155}, s_{155}, t_{155}, a_{155}, s_{16}, b_{155}, c_{155}, d_{155}, e_{155}, f_{156}, g_{156}, h_{156}, i_{156}, j_{156}, k_{156}, f_{17}, l_{156}, m_{156}, n_{156}, p_{156}, q_{156}, r_{156}, s_{156}, t_{156}, a_{156}, b_{156}, i_{17}, c_{156}, d_{156}, e_{156}, f_{157}, g_{157}, h_{157}, i_{157}, j_{157}, k_{157}, l_{157}, l_{17}, m_{157}, n_{157}, p_{157}, q_{157}, r_{157}, s_{157}, t_{157}, a_{157}, b_{157}, c_{157}, p_{17}, d_{157}, e_{157}, f_{158}, g_{158}, h_{158}, i_{158}, j_{158}, k_{158}, l_{158}, m_{158}, s_{17}, n_{158}, p_{158}, q_{158}, r_{158}, s_{158}, t_{158}, a_{158}, b_{158}, c_{158}, d_{158}, b_{17}, e_{158}, f_{159}, g_{159}, h_{159}, 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b_{105}, c_{105}, d_{105}, e_{105}, f_{106}, g_{106}, h_{106}, i_{106}, j_{106}, k_{106}, p_{11}, l_{106}, m_{106}, n_{106}, p_{106}, q_{106}, r_{106}, s_{106}, t_{106}, a_{106}, b_{106}, s_{11}, c_{106}, d_{106}, e_{106}, f_{107}, g_{107}, h_{107}, i_{107}, j_{107}, k_{107}, l_{107}, l, b_{11}, m_{107}, n_{107}, p_{107}, q_{107}, r_{107}, s_{107}, t_{107}, a_{107}, b_{107}, c_{107}, e_{11}, d_{107}, e_{107}, f_{108}, g_{108}, h_{108}, i_{108}, j_{108}, k_{108}, l_{108}, m_{108}, h_{12}, n_{108}, p_{108}, q_{108}, r_{108}, s_{108}, t_{108}, a_{108}, b_{108}, c_{108}, d_{108}, k_{12}, e_{108}, f_{109}, g_{109}, h_{109}, i_{109}, j_{109}, k_{109}, l_{109}, m_{109}, n_{109}, l_{12}, p_{109}, q_{109}, r_{109}, s_{109}, t_{109}, a_{109}, b_{109}, c_{109}, d_{109}, e_{109}, r_{12}, f_{110}, g_{110}, h_{110}, i_{110}, j_{110}, k_{110}, l_{110}, m_{110}, n_{110}, p_{110}, s_{12}, q_{110}, r_{110}, s_{110}, t_{110}, a_{110}, b_{110}, c_{110}, d_{110}, e_{110}, f_{111}, d_{12}, g_{111}, h_{111}, i_{111}, j_{111}, k_{111}, l_{111}, m_{111}, n_{111}, p_{111}, q_{111}, e_{12}, r_{111}, s_{111}, t_{111}, a_{111}, b_{111}, c_{111}, d_{111}, e_{111}, f_{112}, g_{112}, f_{13}, h_{112}, i_{112}, j_{112}, k_{112}, l_{112}, m_{112}, n_{112}, p_{112}, q_{112}, r_{112}, l_1, m_{13}, s_{112}, t_{112}, a_{112}, b_{112}, c_{112}, d_{112}, e_{112}, f_{113}, g_{113}, h_{113}, q_{13}, i_{113}, j_{113}, k_{113}, l_{113}, m_{113}, n_{113}, p_{113}, q_{113}, r_{113}, s_{113}, t_{13}, t_{113}, a_{113}, b_{113}, c_{113}, d_{113}, e_{113}, f_{114}, g_{114}, h_{114}, i_{114}, a_{13}, j_{114}, k_{114}, l_{114}, m_{114}, n_{114}, p_{114}, q_{114}, r_{114}, s_{114}, t_{114}, b_{13}, a_{114}, b_{114}, c_{114}, d_{114}, e_{114}, f_{115}, g_{115}, h_{115}, i_{115}, j_{115}, c_{13}, k_{115}, l_{115}, m_{115}, n_{115}, p_{115}, q_{115}, r_{115}, s_{115}, t_{115}, a_{115}, l_{14}, b_{115}, c_{115}, d_{115}, e_{115}, f_{116}, g_{116}, h_{116}, i_{116}, j_{116}, k_{116}, m_{14}, l_{116}, m_{116}, n_{116}, p_{116}, q_{116}, r_{116}, s_{116}, t_{116}, a_{116}, b_{116}, s_{14}, c_{116}, d_{116}, e_{116}, f_{117}, g_{117}, h_{117}, i_{117}, j_{117}, k_{117}, l_{117}, t_{14}, m_{117}, n_{117}, p_{117}, q_{117}, r_{117}, s_{117}, t_{117}, a_{117}, b_{117}, c_{117}, q_1, e_{14}, d_{117}, e_{117}, f_{118}, g_{118}, h_{118}, i_{118}, j_{118}, k_{118}, l_{118}, m_{118}, f_{15}, n_{118}, p_{118}, q_{118}, r_{118}, s_{118}, t_{118}, a_{118}, b_{118}, c_{118}, d_{118}, g_{15}, e_{118}, f_{119}, g_{119}, h_{119}, i_{119}, j_{119}, k_{119}, l_{119}, m_{119}, n_{119}, h_{15}, p_{119}, q_{119}, r_{119}, s_{119}, t_{119}, a_{119}, b_{119}, c_{119}, d_{119}, e_{119}, r_{15}, f_{120}, g_{120}, h_{120}, i_{120}, j_{120}, k_{120}, l_{120}, m_{120}, n_{120}, p_{120}, a_{15}, q_{120}, r_{120}, s_{120}, t_{120}, a_{120}, b_{120}, c_{120}, d_{120}, e_{120}, f_{121}, d_{15}, g_{121}, h_{121}, i_{121}, b_{152}, c_{152}, d_{152}, e_{152}, f_{153}, g_{153}, h_{153}, g_{16}, i_{153}, j_{153}, k_{153}, l_{153}, m_{153}, n_{153}, p_{153}, q_{153}, r_{153}, s_{153}, h_{16}, t_{153}, a_{153}, b_{153}, c_{153}, d_{153}, e_{153}, f_{154}, g_{154}, h_{154}, i_{154}, m_{16}, j_{154}, k_{154}, l_{154}, m_{154}, n_{154}, p_{154}, q_{154}, r_{154}, s_{154}, t_{154}Polygon(A, C, n) → poly2, m, d_1, t_{16}, b_{197}, c_{197}, d_{197}, e_{197}, f_{198}, g_{198}, h_{198}, i_{198}, j_{198}, k_{198}, a_{16}, l_{198}, m_{198}, n_{198}, p_{198}, q_{198}, r_{198}, s_{198}, t_{198}, a_{198}, b_{198}, b_{16}, c_{198}, d_{198}, e_{198}, f_{199}, g_{199}, h_{199}, i_{199}, j_{199}, k_{199}, l_{199}, g_{17}, m_{199}, n_{199}, p_{199}, q_{199}, r_{199}, s_{199}, t_{199}, a_{199}, b_{199}, c_{199}, j_{17}, d_{199}, e_{199}, f_{200}, g_{200}, h_{200}, i_{200}, j_{200}, k_{200}, l_{200}, m_{200}, m_{17}, n_{200}, p_{200}, q_{200}, r_{200}, s_{200}, t_{200}, a_{200}, b_{200}, c_{200}, d_{200}, q_{17}, e_{200}, f_{201}, g_{201}, h_{201}, i_{201}, j_{201}, k_{201}, l_{201}, m_{201}, n_{201}, t_{17}, p_{201}, q_{201}, r_{201}, s_{201}, t_{201}, a_{201}, b_{201}, c_{201}, d_{201}, e_{201}, d_{17}, f_{202}, g_{202}, h_{202}, i_{202}, j_{202}, k_{202}, l_{202}, m_{202}, n_{202}, p_{202}, e_{17}, q_{202}, r_{202}, s_{202}, t_{202}, a_{202}, b_{202}, c_{202}, d_{202}, e_{202}, f_{203}, g_2, i_{18}, g_{203}, h_{203}, i_{203}, j_{203}, k_{203}, l_{203}, m_{203}, n_{203}, p_{203}, q_{203}, m_{18}, r_{203}, s_{203}, t_{203}, a_{203}, b_{203}, c_{203}, d_{203}, e_{203}, f_{204}, g_{204}, n_{18}, h_{204}, i_{204}, j_{204}, k_{204}, l_{204}, m_{204}, n_{204}, p_{204}, q_{204}, r_{204}, s_{18}, s_{204}, t_{204}, a_{204}, b_{204}, c_{204}, d_{204}, e_{204}, f_{205}, g_{205}, h_{205}, c_{18}, i_{205}, j_{205}, k_{205}, l_{205}, m_{205}, n_{205}, p_{205}, q_{205}, r_{205}, s_{205}, d_{18}, t_{205}, a_{205}, b_{205}, c_{205}, d_{205}, e_{205}, f_{206}, g_{206}, h_{206}, i_{206}, h_{19}, j_{206}, k_{206}, l_{206}, m_{206}, n_{206}, p_{206}, q_{206}, r_{206}, s_{206}, t_{206}, l_{19}, a_{206}, b_{206}, c_{206}, d_{206}, e_{206}, f_{207}, g_{207}, h_{207}, i_{207}, j_{207}, m_{19}, k_{207}, l_{207}, m_{207}, n_{207}, p_{207}, q_{207}, r_{207}, s_{207}, t_{207}, a_{207}, r_{19}, b_{207}, c_{207}, d_{207}, e_{207}, f_{208}, g_{208}, h_{208}, i_{208}, j_{208}, k_{208}, j_2, a_{19}, l_{208}, m_{208}, n_{208}, p_{208}, q_{208}, r_{208}, s_{208}, t_{208}, a_{208}, b_{208}, d_{19}, c_{208}, d_{208}, e_{208}, f_{209}, g_{209}, h_{209}, i_{209}, j_{209}, k_{209}, l_{209}, g_{20}, m_{209}, n_{209}, p_{209}, q_{209}, r_{209}, s_{209}, t_{209}, a_{209}, b_{209}, c_{209}, j_{20}, d_{209}, e_{209}, f_{210}, g_{210}, h_{210}, i_{210}, j_{210}, k_{210}, l_{210}, m_{210}, m_{20}, n_{210}, p_{210}, q_{210}, r_{210}, s_{210}, t_{210}, a_{210}, b_{210}, c_{210}, d_{210}, q_{20}, e_{210}, f_{211}, g_{211}, h_{211}, i_{211}, j_{211}, k_{211}, l_{211}, m_{211}, n_{211}, t_{20}, p_{211}, q_{211}, r_{211}, s_{211}, t_{211}, a_{211}, b_{211}, c_{211}, d_{211}, e_{211}, c_{20}, f_{212}, g_{212}, h_{212}, i_{212}, j_{212}, k_{212}, l_{212}, m_{212}, n_{212}, p_{212}, i_{21}, q_{212}, r_{212}, s_{212}, t_{212}, a_{212}, b_{212}, c_{212}, d_{212}, e_{212}, f_{213}, j_{21}, g_{213}, h_{213}, i_{213}, j_{213}, k_{213}, l_{213}, m_{213}, n_{213}, p_{213}, q_{213}, m_2, k_{21}, r_{213}, s_{213}, t_{213}, a_{213}, b_{213}, c_{213}, d_{213}, e_{213}, f_{214}, g_{214}, l_{21}, h_{214}, i_{214}, j_{214}, k_{214}, l_{214}, m_{214}, n_{214}, p_{214}, q_{214}, r_{214}, s_{21}, s_{214}, t_{214}, a_{214}, b_{214}, c_{214}, d_{214}, e_{214}, f_{215}, g_{215}, h_{215}, b_{21}, i_{215}, j_{215}, k_{215}, l_{215}, m_{215}, n_{215}, p_{215}, q_{215}, r_{215}, s_{215}, e_{21}, t_{215}, a_{215}, b_{215}, c_{215}, d_{215}, e_{215}, f_{216}, g_{216}, h_{216}, i_{216}, h_{22}, j_{216}, k_{216}, l_{216}, m_{216}, n_{216}, p_{216}, q_{216}, r_{216}, s_{216}, t_{216}, k_{22}, a_{216}, b_{216}, c_{216}, d_{216}, e_{216}, f_{217}, g_{217}, h_{217}, i_{217}, j_{217}, n_{22}, k_{217}, l_{217}, m_{217}, n_{217}, p_{217}, q_{217}, r_{217}, s_{217}, t_{217}, a_{217}, r_{22}, b_{217}, c_{217}, d_{217}, e_{217}, f_{218}, g_{218}, h_{218}, i_{218}, j_{218}, k_{218}, a_{22}, l_{218}, m_{218}, n_{218}, p_{218}, q_{218}, r_{218}, s_{218}, t_{218}, a_{218}, b_{218}, q_2, e_{22}, c_{218}, d_{218}, e_{218}, f_{219}, g_{219}, h_{219}, i_{219}, j_{219}, k_{219}, l_{219}, f_{23}, m_{219}, n_{219}, p_{219}, q_{219}, r_{219}, s_{219}, t_{219}, a_{219}, b_{219}, c_{219}, j_{23}, d_{219}, e_{219}, f_{220}, g_{220}, h_{220}, i_{220}, j_{220}, k_{220}, l_{220}, m_{220}, m_{23}, n_{220}, p_{220}, q_{220}, r_{220}, s_{220}, t_{220}, a_{220}, b_{220}, c_{220}, d_{220}, q_{23}, e_{220}, f_{221}, g_{221}, h_{221}, i_{221}, j_{221}, k_{221}, l_{221}, m_{221}, n_{221}, t_{23}, p_{221}, q_{221}, r_{221}, s_{221}, t_{221}, a_{221}, b_{221}, c_{221}, d_{221}, e_{221}, d_{23}, f_{222}, g_{222}, h_{222}, i_{222}, j_{222}, k_{222}, l_{222}, m_{222}, n_{222}, p_{222}, e_{23}, q_{222}, r_{222}, s_{222}, t_{222}, a_{222}, b_{222}, c_{222}, d_{222}, e_{222}, f_{223}, i_{24}, g_{223}, h_{223}, i_{223}, j_{223}, k_{223}, l_{223}, m_{223}, n_{223}, p_{223}, q_{223}, l_{24}, r_{223}, s_{223}, t_{223}, a_{223}, b_{223}, c_{223}, d_{223}, e_{223}, f_{224}, g_{224}, t_2, p_{24}, h_{224}, i_{224}, j_{224}, k_{224}, l_{224}, m_{224}, n_{224}, p_{224}, q_{224}, r_{224}, s_{24}, s_{224}, t_{224}, a_{224}, b_{224}, c_{224}, d_{224}, e_{224}, f_{225}, g_{225}, h_{225}, c_{24}, i_{225}, j_{225}, k_{225}, l_{225}, m_{225}, n_{225}, p_{225}, q_{225}, r_{225}, s_{225}, d_{24}, t_{225}, a_{225}, b_{225}, c_{225}, d_{225}, e_{225}, f_{226}, g_{226}, h_{226}, i_{226}, i_{25}, j_{226}, k_{226}, l_{226}, m_{226}, n_{226}, p_{226}, q_{226}, r_{226}, s_{226}, t_{226}, j_{25}, a_{226}, b_{226}, c_{226}, d_{226}, e_{226}, f_{227}, g_{227}, h_{227}, i_{227}, j_{227}, n_{25}, k_{227}, l_{227}, m_{227}, n_{227}, p_{227}, q_{227}, r_{227}, s_{227}, t_{227}, a_{227}, r_{25}, b_{227}, c_{227}, d_{227}, e_{227}, f_{228}, g_{228}, h_{228}, i_{228}, j_{228}, k_{228}, b_{25}, l_{228}, m_{228}, n_{228}, p_{228}, q_{228}, r_{228}, s_{228}, t_{228}, a_{228}, b_{228}, c_{25}, c_{228}, d_{228}, e_{228}, f_{229}, g_{229}, h_{229}, i_{229}, j_{229}, k_{229}, l_{229}, l_3, g_{26}, m_{229}, n_{229}, p_{229}, q_{229}, r_{229}, s_{229}, t_{229}, a_{229}, b_{229}, c_{229}, k_{26}, d_{229}, e_{229}, f_{230}, g_{230}, h_{230}, i_{230}, j_{230}, k_{230}, l_{230}, m_{230}, l_{26}, n_{230}, p_{230}, q_{230}, r_{230}, s_{230}, t_{230}, a_{230}, b_{230}, c_{230}, d_{230}, q_{26}, e_{230}, f_{231}, g_{231}, h_{231}, i_{231}, j_{231}, k_{231}, l_{231}, m_{231}, n_{231}, a_{26}, p_{231}, q_{231}, r_{231}, s_{231}, t_{231}, a_{231}, b_{231}, c_{231}, d_{231}, e_{231}, b_{26}, f_{232}, g_{232}, h_{232}, i_{232}, j_{232}, k_{232}, l_{232}, m_{232}, n_{232}, p_{232}, f_{27}, q_{232}, r_{232}, s_{232}, t_{232}, a_{232}, b_{232}, c_{232}, d_{232}, e_{232}, f_{233}, i_{27}, g_{233}, h_{233}, i_{233}, j_{233}, k_{233}, l_{233}, m_{233}, n_{233}, p_{233}, q_{233}, l_{27}, r_{233}, s_{233}, t_{233}, a_{233}, b_{233}, c_{233}, d_{233}, e_{233}, f_{234}, g_{234}, p_{27}, h_{234}, i_{234}, j_{234}, k_{234}, l_{234}, m_{234}, n_{234}, p_{234}, q_{234}, r_{234}, p_3, s_{27}, s_{234}, t_{234}, a_{234}, b_{234}, c_{234}, d_{234}, e_{234}, f_{235}, g_{235}, h_{235}, c_{27}, i_{235}, j_{235}, k_{235}, l_{235}, m_{235}, n_{235}, p_{235}, q_{235}, r_{235}, s_{235}, d_{27}, t_{235}, a_{235}, b_{235}, c_{235}, d_{235}, e_{235}, f_{236}, g_{236}, h_{236}, i_{236}, i_{28}, j_{236}, k_{236}, l_{236}, m_{236}, n_{236}, p_{236}, q_{236}, r_{236}, s_{236}, t_{236}, j_{28}, a_{236}, b_{236}, c_{236}, d_{236}, e_{236}, f_{237}, g_{237}, h_{237}, i_{237}, j_{237}, p_{28}, k_{237}, l_{237}, m_{237}, n_{237}, p_{237}, q_{237}, r_{237}, s_{237}, t_{237}, a_{237}, q_{28}, b_{237}, c_{237}, d_{237}, e_{237}, f_{238}, g_{238}, h_{238}, i_{238}, j_{238}, k_{238}, a_{28}, l_{238}, m_{238}, n_{238}, p_{238}, q_{238}, r_{238}, s_{238}, t_{238}, a_{238}, b_{238}, d_{28}, c_{238}, f_{282}, g_{292}, h_{292}, i_{292}, j_{292}, k_{292}, l_{292}, m_{292}, n_{292}, g_{29}, p_{292}, q_{292}, r_{292}, s_{292}, t_{292}, a_{292}, b_{292}, c_{292}, d_{292}, e_{292}, s_3, j_{29}, f_{293}, g_{293}, h_{293}, i_{293}, j_{293}, k_{293}, l_{293}, m_{293}, n_{293}, p_{293}, n_{29}, q_{293}, r_{293}, s_{293}, t_{293}, a_{293}, b_{293}, c_{293}, d_{293}, e_{293}, f_{294}, p_{29}, g_{294}, h_{294}, i_{294}, j_{294}, k_{294}, l_{294}, m_{294}, n_{294}, p_{294}, q_{294}, t_{29}, r_{294}, s_{294}, t_{294}, a_{294}, b_{294}, c_{294}, d_{294}, e_{294}, f_{295}, g_{295}, d_{29}, h_{295}, i_{295}, j_{295}, k_{295}, l_{295}, m_{295}, n_{295}, p_{295}, q_{295}, r_{295}, e_{29}, s_{295}, t_{295}, a_{295}, b_{295}, c_{295}, d_{295}, e_{295}, f_{296}, g_{296}, h_{296}, k_{30}, i_{296}, j_{296}, k_{296}, l_{296}, m_{296}, n_{296}, p_{296}, q_{296}, r_{296}, s_{296}, l_{30}, t_{296}, a_{296}, b_{296}, c_{296}, d_{296}, e_{296}, f_{297}, g_{297}, h_{297}, i_{297}, m_{30}, j_{297}, k_{297}, l_{297}, m_{297}, n_{297}, p_{297}, q_{297}, r_{297}, s_{297}, t_{297}, s_{30}, a_{297}, b_{297}, c_{297}, d_{297}, e_{297}, f_{298}, g_{298}, h_{298}, i_{298}, j_{298}, b_3, b_{30}, k_{298}, l_{298}, m_{298}, n_{298}, p_{298}, q_{298}, r_{298}, s_{298}, t_{298}, a_{298}, e_{30}, b_{298}, c_{298}, d_{298}, e_{298}, f_{299}, g_{299}, h_{299}, i_{299}, j_{299}, k_{299}, h_{31}, l_{299}, m_{299}, n_{299}, p_{299}, q_{299}, r_{299}, s_{299}, t_{299}, a_{299}, b_{299}, k_{31}, c_{299}, d_{299}, e_{299}, f_{300}, g_{300}, h_{300}, i_{300}, j_{300}, k_{300}, l_{300}, n_{31}, m_{300}, n_{300}, p_{300}, q_{300}, r_{300}, s_{300}, t_{300}, a_{300}, b_{300}, c_{300}, s_{31}, d_{300}, e_{300}, f_{301}, g_{301}, h_{301}, i_{301}, j_{301}, k_{301}, l_{301}, m_{301}, t_{31}, n_{301}, p_{301}, q_{301}, r_{301}, s_{301}, t_{301}, a_{301}, b_{301}, c_{301}, d_{301}, e_{31}, e_{301}, p_{312}, q_{312}, r_{312}, s_{312}, t_{312}, a_{312}, b_{312}, c_{312}, d_{312}, f_{32}, 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s_{130}, t_{130}, a_{130}, b_{130}, c_{130}, d_{130}, e_{130}, f_{131}, g_{14}, g_{131}, h_{131}, i_{131}, j_{131}, k_{131}, l_{131}, m_{131}, n_{131}, p_{131}, q_{131}, n_{14}, r_{131}, s_{131}, t_{131}, a_{131}, b_{131}, c_{131}, d_{131}, e_{131}, f_{132}, g_{132}, p_{14}, h_{132}, i_{132}, j_{132}, k_{132}, l_{132}, m_{132}, n_{132}, p_{132}, q_{132}, r_{132}, a_{14}, s_{132}, t_{132}, a_{132}, b_{132}, c_{132}, d_{132}, e_{132}, f_{133}, g_{133}, h_{133}, b_{14}, i_{133}, j_{133}, k_{133}, l_{133}, m_{133}, n_{133}, p_{133}, q_{133}, r_{133}, s_{133}, r_1, i_{15}, t_{133}, a_{133}, b_{133}, c_{133}, d_{133}, e_{133}, f_{134}, g_{134}, h_{134}, i_{134}, j_{15}, j_{134}, k_{134}, l_{134}, m_{134}, n_{134}, p_{134}, q_{134}, r_{134}, s_{134}, t_{134}, k_{15}, a_{134}, b_{134}, c_{134}, d_{134}, e_{134}, f_{135}, g_{135}, h_{135}, i_{135}, j_{135}, l_{15}, k_{135}, l_{135}, m_{135}, n_{135}, p_{135}, q_{135}, r_{135}, s_{135}, t_{135}, a_{135}, s_{15}, b_{135}, c_{135}, d_{135}, e_{135}, f_{136}, g_{136}, h_{136}, i_{136}, j_{136}, k_{136}, b_{15}, l_{136}, m_{136}, n_{136}, p_{136}, q_{136}, r_{136}, s_{136}, t_{136}, a_{136}, b_{136}, e_{15}, c_{136}, d_{136}, e_{136}, c_{195}, d_{195}, e_{195}, f_{196}, g_{196}, h_{196}, i_{196}, i_{16}, j_{196}, k_{196}, l_{196}, m_{196}, n_{196}, p_{196}, q_{196}, r_{196}, s_{196}, t_{196}, j_{16}, a_{196}, b_{196}, c_{196}, d_{196}, e_{196}, f_{197}, g_{197}, h_{197}, i_{197}, j_{197}, n_{16}, k_{197}, l_{197}, m_{197}, n_{197}, p_{197}, q_{197}, r_{197}, s_{197}, t_{197}, a_{197}Polygon(C, B, n) → poly3, b, e_1, c_{16}, c_{240}, d_{240}, e_{240}, f_{241}, g_{241}, h_{241}, i_{241}, j_{241}, k_{241}, l_{241}, d_{16}, m_{241}, n_{241}, p_{241}, q_{241}, r_{241}, s_{241}, t_{241}, a_{241}, b_{241}, c_{241}, e_{16}, d_{241}, e_{241}, f_{242}, g_{242}, h_{242}, i_{242}, j_{242}, k_{242}, l_{242}, m_{242}, h_{17}, n_{242}, p_{242}, q_{242}, r_{242}, s_{242}, t_{242}, a_{242}, b_{242}, c_{242}, d_{242}, k_{17}, e_{242}, 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l_{248}, m_{248}, n_{248}, p_{248}, q_{248}, r_{248}, s_{248}, t_{248}, f_{19}, a_{248}, b_{248}, c_{248}, d_{248}, e_{248}, f_{249}, g_{249}, h_{249}, i_{249}, j_{249}, i_{19}, k_{249}, l_{249}, m_{249}, n_{249}, p_{249}, q_{249}, r_{249}, s_{249}, t_{249}, a_{249}, n_{19}, b_{249}, c_{249}, d_{249}, e_{249}, f_{250}, g_{250}, h_{250}, i_{250}, j_{250}, k_{250}, p_{19}, l_{250}, m_{250}, n_{250}, p_{250}, q_{250}, r_{250}, s_{250}, t_{250}, a_{250}, b_{250}, s_{19}, c_{250}, d_{250}, e_{250}, f_{251}, g_{251}, h_{251}, i_{251}, j_{251}, k_{251}, l_{251}, k_2, b_{19}, m_{251}, n_{251}, p_{251}, q_{251}, r_{251}, s_{251}, t_{251}, a_{251}, b_{251}, c_{251}, e_{19}, d_{251}, e_{251}, f_{252}, g_{252}, h_{252}, i_{252}, j_{252}, k_{252}, l_{252}, m_{252}, h_{20}, n_{252}, p_{252}, q_{252}, r_{252}, s_{252}, t_{252}, a_{252}, b_{252}, c_{252}, d_{252}, k_{20}, e_{252}, f_{253}, g_{253}, h_{253}, i_{253}, j_{253}, k_{253}, l_{253}, m_{253}, n_{253}, n_{20}, p_{253}, q_{253}, r_{253}, s_{253}, t_{253}, a_{253}, b_{253}, c_{253}, d_{253}, e_{253}, r_{20}, f_{254}, g_{254}, h_{254}, i_{254}, j_{254}, k_{254}, l_{254}, m_{254}, n_{254}, p_{254}, a_{20}, q_{254}, r_{254}, s_{254}, t_{254}, a_{254}, b_{254}, c_{254}, d_{254}, e_{254}, f_{255}, d_{20}, g_{255}, h_{255}, i_{255}, j_{255}, k_{255}, l_{255}, m_{255}, n_{255}, p_{255}, q_{255}, m_{21}, r_{255}, s_{255}, t_{255}, a_{255}, b_{255}, c_{255}, d_{255}, e_{255}, f_{256}, g_{256}, n_{21}, h_{256}, i_{256}, j_{256}, k_{256}, l_{256}, m_{256}, n_{256}, p_{256}, q_{256}, r_{256}, n_2, p_{21}, s_{256}, t_{256}, a_{256}, b_{256}, c_{256}, d_{256}, e_{256}, f_{257}, g_{257}, h_{257}, q_{21}, i_{257}, j_{257}, k_{257}, l_{257}, m_{257}, n_{257}, p_{257}, q_{257}, r_{257}, s_{257}, t_{21}, t_{257}, a_{257}, b_{257}, c_{257}, d_{257}, e_{257}, f_{258}, g_{258}, h_{258}, i_{258}, c_{21}, j_{258}, k_{258}, l_{258}, m_{258}, n_{258}, p_{258}, q_{258}, r_{258}, s_{258}, t_{258}, f_{22}, a_{258}, b_{258}, c_{258}, d_{258}, e_{258}, f_{259}, g_{259}, h_{259}, i_{259}, j_{259}, i_{22}, k_{259}, l_{259}, m_{259}, n_{259}, p_{259}, q_{259}, r_{259}, s_{259}, t_{259}, a_{259}, l_{22}, b_{259}, c_{259}, d_{259}, e_{259}, f_{260}, g_{260}, h_{260}, i_{260}, j_{260}, k_{260}, p_{22}, l_{260}, m_{260}, n_{260}, p_{260}, q_{260}, r_{260}, s_{260}, t_{260}, a_{260}, b_{260}, s_{22}, c_{260}, d_{260}, e_{260}, f_{261}, g_{261}, h_{261}, i_{261}, j_{261}, k_{261}, l_{261}, b_{22}, m_{261}, n_{261}, p_{261}, q_{261}, r_{261}, s_{261}, t_{261}, a_{261}, b_{261}, c_{261}, r_2, g_{23}, d_{261}, e_{261}, f_{262}, g_{262}, h_{262}, i_{262}, j_{262}, k_{262}, l_{262}, m_{262}, h_{23}, n_{262}, p_{262}, q_{262}, r_{262}, s_{262}, t_{262}, a_{262}, b_{262}, c_{262}, d_{262}, k_{23}, e_{262}, f_{263}, g_{263}, h_{263}, i_{263}, j_{263}, k_{263}, l_{263}, m_{263}, n_{263}, n_{23}, p_{263}, q_{263}, r_{263}, s_{263}, t_{263}, a_{263}, b_{263}, c_{263}, d_{263}, e_{263}, r_{23}, f_{264}, g_{264}, h_{264}, i_{264}, j_{264}, 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A_{205}, B_{205}, C_{205}, D_{205}, E_{205}, F_{205}, r_{55}, G_{205}, H_{205}, I_{205}, J_{205}, K_{205}, L_{205}, M_{205}, N_{205}, O_{205}, P_{205}, s_{55}, Q_{205}, R_{205}, S_{205}, T_{205}, U_{205}, V_{205}, W_{205}, Z_{205}, A_{206}, B_{206}, t_{55}, C_{206}, D_{206}, E_{206}, F_{206}, G_{206}, H_{206}, I_{206}, J_{206}, K_{206}, L_{206}, a_{55}, M_{206}, N_{206}, O_{206}, P_{206}, Q_{206}, R_{206}, S_{206}, T_{206}, U_{206}, V_{206}, q_6, b_{55}, W_{206}, Z_{206}, A_{207}, B_{207}, C_{207}, D_{207}, E_{207}, F_{207}, G_{207}, H_{207}, c_{55}, I_{207}, J_{207}, K_{207}, L_{207}, M_{207}, N_{207}, O_{207}, P_{207}, Q_{207}, R_{207}, d_{55}, S_{207}, T_{207}, U_{207}, V_{207}, W_{207}, Z_{207}, A_{208}, B_{208}, C_{208}, D_{208}, e_{55}, E_{208}, F_{208}, G_{208}, H_{208}, I_{208}, J_{208}, K_{208}, L_{208}, M_{208}, N_{208}, f_{56}, O_{208}, P_{208}, Q_{208}, R_{208}, S_{208}, T_{208}, U_{208}, V_{208}, W_{208}, Z_{208}, g_{56}, A_{209}, B_{209}, C_{209}, D_{209}, E_{209}, F_{209}, G_{209}, H_{209}, I_{209}, J_{209}, h_{56}, K_{209}, L_{209}, M_{209}, N_{209}, O_{209}, P_{209}, Q_{209}, R_{209}, S_{209}, T_{209}, i_{56}, U_{209}, V_{209}, W_{209}, Z_{209}, A_{210}, B_{210}, C_{210}, D_{210}, E_{210}, F_{210}, j_{56}, G_{210}, H_{210}, I_{210}, J_{210}, K_{210}, L_{210}, M_{210}, N_{210}, O_{210}, P_{210}, k_{56}, Q_{210}, R_{210}, S_{210}, T_{210}, U_{210}, V_{210}, W_{210}, Z_{210}, A_{211}, B_{211}, r_6, l_{56}, C_{211}, D_{211}, E_{211}, F_{211}, G_{211}, H_{211}, I_{211}, J_{211}, K_{211}, L_{211}, m_{56}, M_{211}, N_{211}, O_{211}, P_{211}, Q_{211}, R_{211}, S_{211}, T_{211}, U_{211}, V_{211}, n_{56}, W_{211}, Z_{211}, A_{212}, B_{212}, C_{212}, D_{212}, E_{212}, F_{212}, G_{212}, H_{212}, k_{72}, I_{212}, J_{212}, K_{212}, L_{212}, M_{212}, N_{212}, O_{212}, P_{212}, Q_{212}, R_{212}, l_{72}, S_{212}, T_{212}, U_{212}, V_{212}, W_{212}, Z_{212}, A_{213}, B_{213}, C_{213}, D_{213}, m_{72}, E_{213}, F_{213}, G_{213}, H_{213}, I_{213}, J_{213}, K_{213}, L_{213}, M_{213}, N_{213}, n_{72}, O_{213}, P_{213}, Q_{213}, R_{213}, S_{213}, T_{213}, U_{213}, V_{213}, W_{213}, Z_{213}, p_{72}, A_{214}, B_{214}, C_{214}, D_{214}, E_{214}, F_{214}, G_{214}, H_{214}, I_{214}, J_{214}, q_{72}, K_{214}, L_{214}, M_{214}, N_{214}, O_{214}, P_{214}, Q_{214}, R_{214}, S_{214}, T_{214}, r_{72}, U_{214}, V_{214}, W_{214}, Z_{214}, A_{215}, B_{215}, C_{215}, D_{215}, E_{215}, F_{215}, s_6, s_{72}, G_{215}, H_{215}, I_{215}, J_{215}, K_{215}, L_{215}, M_{215}, N_{215}, O_{215}, P_{215}, t_{72}, Q_{215}, R_{215}, S_{215}, T_{215}, U_{215}, V_{215}, W_{215}, Z_{215}, A_{216}, B_{216}, a_{72}, C_{216}, D_{216}, E_{216}, F_{216}, G_{216}, H_{216}, I_{216}, J_{216}, K_{216}, L_{216}, b_{72}, M_{216}, N_{216}, O_{216}, P_{216}, Q_{216}, R_{216}, S_{216}, T_{216}, U_{216}, V_{216}, c_{72}, W_{216}, Z_{216}, A_{217}, B_{217}, C_{217}, D_{217}, E_{217}, F_{217}, G_{217}, H_{217}, d_{72}, I_{217}, J_{217}, K_{217}, L_{217}, M_{217}, N_{217}, O_{217}, P_{217}, Q_{217}, R_{217}, e_{72}, S_{217}, T_{217}, U_{217}, V_{217}, W_{217}, Z_{217}, A_{218}, B_{218}, C_{218}, D_{218}, f_{73}, E_{218}, F_{218}, G_{218}, H_{218}, I_{218}, J_{218}, K_{218}, L_{218}, M_{218}, N_{218}, g_{73}, O_{218}, P_{218}, Q_{218}, R_{218}, S_{218}, T_{218}, U_{218}, V_{218}, W_{218}, Z_{218}, h_{73}, A_{219}, B_{219}, C_{219}, D_{219}, E_{219}, F_{219}, G_{219}, H_{219}, I_{219}, J_{219}, t_6, i_{73}, K_{219}, L_{219}, M_{219}, N_{219}, O_{219}, P_{219}, Q_{219}, R_{219}, S_{219}, T_{219}, j_{73}, U_{219}, V_{219}, W_{219}, Z_{219}, A_{220}, B_{220}, C_{220}, D_{220}, E_{220}, F_{220}, k_{73}, G_{220}, H_{220}, I_{220}, J_{220}, K_{220}, L_{220}, M_{220}, N_{220}, O_{220}, P_{220}, l_{73}, Q_{220}, R_{220}, S_{220}, T_{220}, U_{220}, V_{220}, W_{220}, Z_{220}, A_{221}, B_{221}, m_{73}, C_{221}, D_{221}, E_{221}, F_{221}, G_{221}, H_{221}, I_{221}, J_{221}, K_{221}, L_{221}, n_{73}, M_{221}, N_{221}, O_{221}, P_{221}, Q_{221}, R_{221}, S_{221}, T_{221}, U_{221}, V_{221}, p_{73}, W_{221}, Z_{221}, A_{222}, B_{222}, C_{222}, D_{222}, E_{222}, F_{222}, G_{222}, H_{222}, q_{73}, I_{222}, J_{222}, K_{222}, L_{222}, M_{222}, N_{222}, O_{222}, P_{222}, Q_{222}, T_{222}, r_{73}, O_{238}, P_{238}, Q_{238}, R_{238}, S_{238}, T_{238}, U_{238}, V_{238}, W_{238}, Z_{238}, s_{73}, A_{239}, B_{239}, C_{239}, D_{239}, E_{239}, F_{239}, G_{239}, H_{239}, I_{239}, J_{239}, c_6, t_{73}, K_{239}, L_{239}, M_{239}, N_{239}, O_{239}, P_{239}, Q_{239}, R_{239}, S_{239}, T_{239}, a_{73}, U_{239}, V_{239}, W_{239}, Z_{239}, A_{240}, B_{240}, C_{240}, D_{240}, E_{240}, F_{240}, b_{73}, G_{240}, H_{240}, I_{240}, J_{240}, K_{240}, L_{240}, M_{240}, N_{240}, O_{240}, P_{240}, c_{73}, Q_{240}, R_{240}, S_{240}, T_{240}, U_{240}, V_{240}, W_{240}, Z_{240}, A_{241}, B_{241}, d_{73}, C_{241}, D_{241}, E_{241}, F_{241}, G_{241}, H_{241}, I_{241}, J_{241}, K_{241}, L_{241}, e_{73}, M_{241}, N_{241}, O_{241}, P_{241}, Q_{241}, R_{241}, S_{241}, T_{241}, U_{241}, V_{241}, f_{74}, W_{241}, Z_{241}, A_{242}, B_{242}, C_{242}, D_{242}, E_{242}, F_{242}, G_{242}, H_{242}, g_{74}, I_{242}, J_{242}, K_{242}, L_{242}, M_{242}, N_{242}, O_{242}, P_{242}, Q_{242}, R_{242}, h_{74}, S_{242}, T_{242}, U_{242}, V_{242}, W_{242}, Z_{242}, A_{243}, B_{243}, C_{243}, D_{243}, i_{74}, E_{243}, F_{243}, G_{243}, H_{243}, I_{243}, J_{243}, K_{243}, L_{243}, M_{243}, N_{243}, h_7, j_{74}, O_{243}, P_{243}, Q_{243}, R_{243}, S_{243}, T_{243}, U_{243}, V_{243}, W_{243}, Z_{243}, k_{74}, A_{244}, B_{244}, C_{244}, D_{244}, E_{244}, F_{244}, G_{244}, H_{244}, I_{244}, J_{244}, l_{74}, K_{244}, L_{244}, M_{244}, N_{244}, O_{244}, P_{244}, Q_{244}, R_{244}, S_{244}, T_{244}, m_{74}, U_{244}, V_{244}, W_{244}, Z_{244}, A_{245}, B_{245}, C_{245}, D_{245}, E_{245}, F_{245}, n_{74}, G_{245}, H_{245}, I_{245}, J_{245}, K_{245}, L_{245}, M_{245}, N_{245}, O_{245}, P_{245}, p_{74}, Q_{245}, R_{245}, S_{245}, T_{245}, U_{245}, V_{245}, W_{245}, Z_{245}, A_{246}, B_{246}, q_{74}, C_{246}, D_{246}, E_{246}, F_{246}, G_{246}, H_{246}, I_{246}, J_{246}, K_{246}, H_{247}, r_{74}, I_{247}, J_{247}, K_{247}, L_{247}, M_{247}, N_{247}, O_{247}, P_{247}, Q_{247}, J_{249}, s_{74}, K_{249}, L_{249}, M_{249}, N_{249}, O_{249}, P_{249}, Q_{249}, R_{249}, S_{249}, T_{249}, t_{74}, U_{249}, V_{249}, W_{249}, Z_{249}, A_{250}, B_{250}, C_{250}, D_{250}, E_{250}, e, i_7, a_{74}, b_{74}, c_{74}, d_{74}, e_{74}, f_{75}, g_{75}, h_{75}, i_{75}, j_{75}, l_7, k_{75}, l_{75}, m_{75}, n_{75}, p_{75}, q_{75}, r_{75}, s_{75}, t_{75}, a_{75}, p_7, b_{75}, c_{75}, d_{75}, e_{75}, f_{76}, g_{76}, h_{76}, i_{76}, j_{76}, k_{76}, s_7, l_{76}, m_{76}, n_{76}, p_{76}, q_{76}, r_{76}, s_{76}, t_{76}, a_{76}, b_{76}, b_7, c_{76}, d_{76}, e_{76}, f_{77}, g_{77}, h_{77}, i_{77}, j_{77}, k_{77}, l_{77}, e_7, m_{77}, n_{77}, p_{77}, q_{77}, r_{77}, s_{77}, t_{77}, a_{77}, b_{77}, c_{77}, h_8, d_{77}, e_{77}, f_{78}, g_{78}, h_{78}, i_{78}, j_{78}, k_{78}, l_{78}, m_{78}, k_8, n_{78}, p_{78}, q_{78}, r_{78}, s_{78}, t_{78}, a_{78}, b_{78}, c_{78}, d_{78}, n_8, e_{78}, f_{79}, g_{79}, h_{79}, i_{79}, j_{79}, k_{79}, l_{79}, m_{79}, n_{79}, r_8, p_{79}, q_{79}, r_{79}, s_{79}, t_{79}, a_{79}, b_{79}, c_{79}, d_{79}, e_{79}, f_1, a_8, f_{80}, g_{80}, h_{80}, f_{97}, g_{97}, h_{97}, i_{97}, j_{97}, k_{97}, l_{97}, f_9, m_{97}, n_{97}, p_{97}, q_{97}, r_{97}, s_{97}, t_{97}, a_{97}, b_{97}, c_{97}, g_9, d_{97}, e_{97}, f_{98}, g_{98}, h_{98}, i_{98}, j_{98}, k_{98}, l_{98}, m_{98}, j_9, n_{98}, p_{98}, q_{98}, r_{98}, s_{98}, t_{98}, a_{98}, b_{98}, c_{98}, d_{98}, m_9, e_{98}, f_{99}, g_{99}, h_{99}, i_{99}, j_{99}, k_{99}, l_{99}, m_{99}, n_{99}, q_9, p_{99}, q_{99}, r_{99}, s_{99}, t_{99}, a_{99}, b_{99}, c_{99}, d_{99}, e_{99}, t_9, f_{100}, g_{100}, h_{100}, i_{100}, j_{100}, k_{100}, l_{100}, m_{100}, n_{100}, p_{100}, c_9, q_{100}, r_{100}, s_{100}, t_{100}, a_{100}, b_{100}, c_{100}, d_{100}, e_{100}, f_{101}, f_{10}, g_{101}, h_{101}, i_{101}, j_{101}, k_{101}, l_{101}, m_{101}, n_{101}, p_{101}, q_{101}, i_{10}, r_{101}, s_{101}, t_{101}, a_{101}, b_{101}, c_{101}, d_{101}, e_{101}, f_{102}, g_{102}, g_1, n_{10}, h_{102}, i_{102}, j_{102}, k_{102}, l_{102}, m_{102}, n_{102}, p_{102}, q_{102}, r_{102}, p_{10}, s_{102}, t_{102}, a_{102}, b_{102}, c_{102}, d_{102}, e_{102}, f_{103}, g_{103}, h_{103}, s_{10}, i_{103}, j_{103}, k_{103}, l_{103}, m_{103}, n_{103}, p_{103}, q_{103}, r_{103}, s_{103}, b_{10}, t_{103}, a_{103}, b_{103}, c_{103}, d_{103}, e_{103}, f_{104}, g_{104}, h_{104}, i_{104}, e_{10}, j_{104}, k_{104}, l_{104}, m_{104}, n_{104}, p_{104}, q_{104}, r_{104}, s_{104}, t_{104}, h_{11}, a_{104}, b_{104}, c_{104}, d_{104}, e_{104}, f_{105}, g_{105}, h_{105}, i_{105}, j_{105}, k_{11}, k_{105}, l_{105}, m_{105}, f_{137}, g_{137}, h_{137}, i_{137}, j_{137}, k_{137}, l_{137}, n_{11}, m_{137}, n_{137}, p_{137}, q_{137}, r_{137}, s_{137}, t_{137}, a_{137}, b_{137}, c_{137}, r_{11}, d_{137}, e_{137}, f_{138}, g_{138}, h_{138}, i_{138}, j_{138}, k_{138}, l_{138}, m_{138}, a_{11}, n_{138}, p_{138}, q_{138}, r_{138}, s_{138}, t_{138}, a_{138}, b_{138}, c_{138}, d_{138}, h_1, d_{11}, e_{138}, f_{139}, g_{139}, h_{139}, i_{139}, j_{139}, k_{139}, l_{139}, m_{139}, n_{139}, g_{12}, p_{139}, q_{139}, r_{139}, s_{139}, t_{139}, a_{139}, b_{139}, c_{139}, d_{139}, e_{139}, j_{12}, f_{140}, g_{140}, h_{140}, i_{140}, j_{140}, k_{140}, l_{140}, m_{140}, n_{140}, p_{140}, p_{12}, q_{140}, r_{140}, s_{140}, t_{140}, a_{140}, b_{140}, c_{140}, d_{140}, e_{140}, f_{141}, q_{12}, g_{141}, h_{141}, i_{141}, j_{141}, k_{141}, l_{141}, m_{141}, n_{141}, p_{141}, q_{141}, b_{12}, r_{141}, s_{141}, t_{141}, a_{141}, b_{141}, c_{141}, d_{141}, e_{141}, f_{142}, g_{142}, c_{12}, h_{142}, i_{142}, j_{142}, k_{142}, l_{142}, m_{142}, n_{142}, p_{142}, q_{142}, r_{142}, j_{13}, s_{142}, t_{142}, a_{142}, b_{142}, c_{142}, d_{142}, e_{142}, f_{143}, g_{143}, h_{143}, k_{13}, i_{143}, j_{143}, k_{143}, l_{143}, m_{143}, n_{143}, p_{143}, q_{143}, r_{143}, s_{143}, l_{13}, t_{143}, a_{143}, b_{143}, c_{143}, d_{143}, e_{143}, f_{144}, g_{144}, h_{144}, i_{144}, p_1, p_{13}, j_{144}, k_{144}, l_{144}, m_{144}, n_{144}, p_{144}, q_{144}, r_{144}, s_{144}, t_{144}, s_{13}, a_{144}, b_{144}, c_{144}, d_{144}, e_{144}, f_{145}, g_{145}, h_{145}, i_{145}, j_{145}, h_{14}, k_{145}, l_{145}, m_{145}, n_{145}, p_{145}, q_{145}, r_{145}, s_{145}, t_{145}, a_{145}, i_{14}, b_{145}, c_{145}, d_{145}, e_{145}, f_{146}, g_{146}, h_{146}, i_{146}, j_{146}, k_{146}, j_{14}, l_{146}, m_{146}, n_{146}, p_{146}, q_{146}, r_{146}, s_{146}, t_{146}, a_{146}, b_{146}, k_{14}, c_{146}, d_{146}, e_{146}, f_{147}, g_{147}, h_{147}, i_{147}, j_{147}, k_{147}, l_{147}, q_{14}, m_{147}, n_{147}, p_{147}, q_{147}, r_{147}, s_{147}, t_{147}, a_{147}, b_{147}, c_{147}, r_{14}, d_{147}, e_{147}, f_{148}, g_{148}, h_{148}, i_{148}, j_{148}, k_{148}, l_{148}, m_{148}, c_{14}, n_{148}, p_{148}, q_{148}, r_{148}, s_{148}, t_{148}, a_{148}, b_{148}, c_{148}, d_{148}, d_{14}, e_{148}, f_{149}, g_{149}, h_{149}, i_{149}, j_{149}, k_{149}, l_{149}, m_{149}, n_{149}, s_1, m_{15}, p_{149}, q_{149}, r_{149}, s_{149}, t_{149}, a_{149}, b_{149}, c_{149}, d_{149}, e_{149}, n_{15}, f_{150}, g_{150}, h_{150}, i_{150}, j_{150}, k_{150}, l_{150}, m_{150}, n_{150}, p_{150}, p_{15}, q_{150}, r_{150}, s_{150}, t_{150}, a_{150}, b_{150}, c_{150}, d_{150}, e_{150}, f_{151}, q_{15}, g_{151}, h_{151}, i_{151}, j_{151}, k_{151}, l_{151}, m_{151}, n_{151}, p_{151}, q_{151}, t_{15}, r_{151}, s_{151}, t_{151}, a_{151}, b_{151}, c_{151}, d_{151}, e_{151}, f_{152}, g_{152}, c_{15}, h_{152}, i_{152}, j_{152}, k_{152}, l_{152}, m_{152}, n_{152}, p_{152}, q_{152}, r_{152}, f_{16}, s_{152}, t_{152}, a_{152}, d_{238}, e_{238}, f_{239}, g_{239}, h_{239}, i_{239}, j_{239}, k_{16}, k_{239}, l_{239}, m_{239}, n_{239}, p_{239}, q_{239}, r_{239}, s_{239}, t_{239}, a_{239}, l_{16}, b_{239}, c_{239}, d_{239}, e_{239}, f_{240}, g_{240}, h_{240}, i_{240}, j_{240}, k_{240}, p_{16}, l_{240}, m_{240}, n_{240}, p_{240}, q_{240}, r_{240}, s_{240}, t_{240}, a_{240}, b_{240}Centroid(poly2) → SCentroid(poly1) → TCentroid(poly3) → WLine(T, C) → i_1Line(W, A) → j_1Line(B, S) → k_1Intersect(k_1, j_1) → Z_1AngularBisector(a_1, c_1) → b_2, c_2AngularBisector(a_1, b_1) → d_2, e_2Mirror(j_1, c_2) → f_3Mirror(k_1, e_2) → g_3Intersect(f_3, g_3) → A_2Line(Z_1, A_2) → h_3Intersect(m_1, h_3) → B_2Segment(B_2, U) → i_3Segment(U, V) → j_3Centroid(poly1) → F_{250}Angle(A, B, F_{250}) → α
AI Drawing Prompt Reference
Draw a triangle with its orthocenter and circumcenter, and connect these two centers with a line. Construct three new triangles outward on the three sides of the original triangle, and find the centroid of each new triangle. Connect each centroid to the opposite vertex of the original triangle, forming three lines that intersect at a common point. Construct the angle bisectors of two interior angles of the original triangle, reflect two of the centroid-vertex lines across these bisectors, and mark the intersection of the two reflected lines. Connect this intersection point with the previous common point, and let this line meet the line joining the orthocenter and circumcenter. Finally, draw segments from this meeting point to the orthocenter and circumcenter, and label an angle formed by a vertex of the original triangle and one of the centroids.
The prompt above was compiled from the original drawing commands and is for reference only.