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六种三角函数与勾股恒等式在单位圆上的几何展示

六种三角函数与勾股恒等式在单位圆上的几何展示
几何画板及绘图内容加载中，请稍等……
2014-01-25 08:07
圆函数三角函数几何作图
①本范例通过单位圆直观演示六种三角函数的几何表示；②涉及核心数学概念：三角函数定义、单位圆、勾股定理、恒等式推导；③构造要点：使用 GeoGebra 命令如 Intersect（交点）、Point（点）、Circle（圆）、Angle（角）、Segment（线段）、OrthogonalLine（垂线）、Distance（距离）、AttachCopyToView（视图复制）等；④适合高中数学教学，用于理解三角函数与单位圆关系及恒等式推导。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → O
  2. Point(yAxis) → B_1
  3. Circle(O, B_1) → c
  4. Intersect(c, xAxis, 2) → D_1
  5. Angle(D_1, O, C) → θ
  6. Segment(O, C) → a_1
  7. Segment(O, D_1) → b
  8. OrthogonalLine(C, a_1) → d
  9. OrthogonalLine(O, b) → e
  10. OrthogonalLine(C, b) → f
  11. Intersect(f, b) → A
  12. Segment(C, A) → A_1
  13. Intersect(d, xAxis) → D
  14. Intersect(d, e) → B
  15. Segment(B, D) → g
  16. Distance(O, C) → distanceGC
  17. Point(a_1) → E
  18. Angle(C, A, O) → α
  19. Angle(O, C, D) → β
  20. Segment(O, A) → h
  21. 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(2.580020231605083, -0.2333304108222177), (2.616316097274854, -0.2333304108222177), (2.661685929362068, -0.2333304108222177), (2.6979817950318394, -0.2333304108222177), (2.752425593536496, -0.2333304108222177), (2.7887214592062675, -0.2333304108222177), (2.825017324876039, -0.2333304108222177), (2.8703871569632526, -0.2333304108222177), (2.915756989050467, -0.2333304108222177), (2.961126821137681, -0.2333304108222177), (3.006496653224895, -0.2333304108222177), (3.0427925188946663, -0.2333304108222177), (3.0881623509818805, -0.2333304108222177), (3.124458216651652, -0.2333304108222177), (3.160754082321423, -0.2333304108222177), (3.206123914408637, -0.2333304108222177), (NaN, NaN), (3.3422334106702793, -0.08814694814313193), (3.3876032427574936, -0.09722091456057479), (3.4057511755923793, -0.12444281381290337), (3.4238991084272645, -0.15166471306523197), (3.44204704126215, -0.17888661231756053), (3.4148251420098217, -0.21518247798733198), (3.3876032427574936, -0.2333304108222177), (3.360381343505165, -0.24240437723966057), (3.3876032427574936, -0.22425644440477485), (3.4148251420098217, -0.21518247798733198), (3.44204704126215, -0.20610851156988913), (3.4692689405144788, -0.19703454515244626), (3.50556480618425, -0.19703454515244626), (3.550934638271464, -0.1879605787350034), (3.5872305039412353, -0.1879605787350034), (3.6235263696110067, -0.1879605787350034), (3.659822235280778, -0.1879605787350034), (3.696118100950549, -0.1879605787350034), (3.7324139666203204, -0.1879605787350034), (3.768709832290092, -0.1879605787350034), (3.805005697959863, -0.1879605787350034), (3.850375530047077, -0.1879605787350034), (3.8866713957168484, -0.17888661231756053), (3.913893294969177, -0.1698126459001177), (3.9592631270563907, -0.1698126459001177), (3.9864850263087193, -0.1607386794826748), (4.040928824813376, -0.1607386794826748), (4.068150724065704, -0.15166471306523197), (4.1225945225703615, -0.15166471306523197), (4.167964354657576, -0.13351678023034624), (4.204260220327347, -0.13351678023034624), (4.231482119579676, -0.12444281381290337), true], 1, (-2.6193625255896515, -4.271245466584291), (8.351062873098714, 1.6994244360931117), (2.000000000000007, 658), (1211, -1.1102230246251565E-15)) → stroke5
  22. AttachCopyToView(PolyLine[(3.904819328551734, -0.11536884739546051), (3.9592631270563907, -0.11536884739546051), (4.013706925561048, -0.11536884739546051), (4.050002791230819, -0.11536884739546051), (4.095372623318033, -0.11536884739546051), (4.14981642182269, -0.11536884739546051), (4.1861122874924614, -0.11536884739546051), (4.231482119579676, -0.11536884739546051), (4.27685195166689, -0.11536884739546051), (4.31314781733666, -0.11536884739546051), (4.349443683006432, -0.11536884739546051), (4.394813515093646, -0.11536884739546051), (4.449257313598303, -0.11536884739546051), (4.4855531792680745, -0.11536884739546051), (4.521849044937846, -0.11536884739546051), (4.558144910607617, -0.12444281381290337), (4.594440776277388, -0.12444281381290337), (4.630736641947159, -0.13351678023034624), (4.657958541199488, -0.1425907466477891), (4.657958541199488, -0.17888661231756053), (4.685180440451816, -0.1879605787350034), (NaN, NaN), (4.31314781733666, -0.2333304108222177), (4.349443683006432, -0.2333304108222177), (4.403887481511089, -0.2333304108222177), (4.458331280015746, -0.2333304108222177), (4.512775078520403, -0.2333304108222177), (4.549070944190174, -0.2333304108222177), (4.585366809859945, -0.2333304108222177), (4.639810608364602, -0.2333304108222177), (4.685180440451816, -0.2333304108222177), (4.721476306121588, -0.2333304108222177), (4.757772171791359, -0.2333304108222177), (4.79406803746113, -0.2333304108222177), (4.839437869548345, -0.2333304108222177), (4.884807701635558, -0.2333304108222177), (4.930177533722772, -0.2333304108222177), (4.966473399392544, -0.2333304108222177), (5.002769265062315, -0.2333304108222177), (5.048139097149529, -0.22425644440477485), (5.084434962819301, -0.22425644440477485), (5.111656862071629, -0.21518247798733198), (5.1570266941588425, -0.20610851156988913), (5.193322559828614, -0.19703454515244626), (5.247766358333271, -0.19703454515244626), (5.2749882575855995, -0.1879605787350034), (5.311284123255371, -0.1879605787350034), (NaN, NaN), (4.902955634470444, -0.11536884739546051), (4.9755473658099865, -0.11536884739546051), (5.0299911643146435, -0.11536884739546051), (5.066287029984415, -0.11536884739546051), (5.111656862071629, -0.11536884739546051), (5.1570266941588425, -0.11536884739546051), (5.202396526246057, -0.11536884739546051), (5.256840324750714, -0.11536884739546051), (5.293136190420485, -0.11536884739546051), (5.3385060225076995, -0.11536884739546051), (5.383875854594914, -0.11536884739546051), (5.420171720264684, -0.11536884739546051), (5.456467585934456, -0.11536884739546051), (5.50183741802167, -0.11536884739546051), (5.547207250108884, -0.12444281381290337), (5.583503115778655, -0.13351678023034624), (5.6379469142833125, -0.13351678023034624), (5.683316746370526, -0.13351678023034624), (5.710538645622854, -0.1425907466477891), (5.746834511292626, -0.1425907466477891), (5.801278309797283, -0.1425907466477891), (5.846648141884497, -0.1425907466477891), (5.873870041136826, -0.15166471306523197), (NaN, NaN), (5.238692391915828, -0.22425644440477485), (5.2749882575855995, -0.22425644440477485), (5.311284123255371, -0.22425644440477485), (5.356653955342585, -0.22425644440477485), (5.411097753847241, -0.22425644440477485), (5.465541552351898, -0.22425644440477485), (5.5199853508565555, -0.22425644440477485), (5.56535518294377, -0.22425644440477485), (5.619798981448427, -0.22425644440477485), (5.656094847118198, -0.22425644440477485), (5.701464679205412, -0.22425644440477485), (5.746834511292626, -0.22425644440477485), (5.79220434337984, -0.22425644440477485), (5.828500209049611, -0.21518247798733198), (5.873870041136826, -0.20610851156988913), (5.91923987322404, -0.20610851156988913), (5.95553573889381, -0.19703454515244626), (5.991831604563582, -0.19703454515244626), (6.028127470233353, -0.19703454515244626), (NaN, NaN), (5.8829440075542685, -0.11536884739546051), (5.91923987322404, -0.11536884739546051), (5.95553573889381, -0.11536884739546051), (5.991831604563582, -0.11536884739546051), (6.037201436650796, -0.11536884739546051), (6.073497302320567, -0.11536884739546051), (NaN, NaN), (3.8866713957168484, -0.22425644440477485), (3.9320412278040626, -0.22425644440477485), (3.9774110598912764, -0.22425644440477485), (4.013706925561048, -0.22425644440477485), (4.050002791230819, -0.22425644440477485), (4.095372623318033, -0.22425644440477485), (4.131668488987804, -0.22425644440477485), (4.167964354657576, -0.22425644440477485), (4.204260220327347, -0.22425644440477485), true], 1, (-2.6193625255896515, -3.9718045748086768), (6.137015067242667, 1.6994244360931117), (0, 625), (965, 0)) → stroke7
  23. AttachCopyToView(PolyLine[(-1.6303001860883846, 1.1912823167163114), (-0.3780928204812758, 0.5833265667476397), (-0.3780928204812758, 0.5470307010778683), (-0.3780928204812758, 0.5107348354080968), (-0.3780928204812758, 0.4653650033208826), (-0.369018854063833, 0.438143104068554), (-0.35994488764639015, 0.40184723839878256), (-0.3327229883940617, 0.3927732719813397), (-0.29642712272429045, 0.4109212048162254), (-0.2782791898894048, 0.438143104068554), (-0.26013125705451917, 0.4653650033208826), (-0.2510572906370764, 0.501660868990654), (-0.24198332421963356, 0.5288827682429826), (-0.23290935780219074, 0.5561046674953112), (-0.20568745854986228, 0.565178633912754), (-0.19661349213241947, 0.5379567346604255), (-0.18753952571497665, 0.501660868990654), (-0.17846555929753383, 0.4653650033208826), (-0.17846555929753383, 0.42906913765111115), (-0.169391592880091, 0.4562910369034397), (-0.169391592880091, 0.49258690257321114), (-0.169391592880091, 0.5288827682429826), (-0.169391592880091, 0.49258690257321114), (-0.169391592880091, 0.4562910369034397), (NaN, NaN), (-0.3327229883940617, 0.5561046674953112), (-0.29642712272429045, 0.5561046674953112), (-0.24198332421963356, 0.5561046674953112), (-0.20568745854986228, 0.5561046674953112), (-0.169391592880091, 0.5561046674953112), (-0.1603176264626482, 0.5288827682429826), (-0.1603176264626482, 0.4835129361557683), (-0.1603176264626482, 0.44721707048599685), (-0.1603176264626482, 0.4109212048162254), (-0.1603176264626482, 0.37462533914645396), (-0.18753952571497665, 0.3655513727290111), (-0.2147614249673051, 0.3927732719813397), (-0.23290935780219074, 0.41999517123366825), (-0.269205223471962, 0.41999517123366825), (NaN, NaN), (-0.1149477943754341, 0.6286963988348541), (-0.1149477943754341, 0.5924005331650827), (-0.1149477943754341, 0.5561046674953112), (-0.12402176079287693, 0.5288827682429826), (-0.12402176079287693, 0.49258690257321114), (-0.12402176079287693, 0.4562910369034397), true], 1, (-2.6193625255896515, -3.9718045748086768), (6.137015067242667, 1.6994244360931117), (0, 625), (965, 0)) → stroke1
  24. AttachCopyToView(PolyLine[(-0.47790645107314683, -0.4238837055885178), (-0.44161058540337556, -0.46017957125828923), (-0.41438868615104707, -0.48740147051061783), (-0.39624075331616143, -0.5146233697629464), (-0.369018854063833, -0.5236973361803893), (-0.35994488764639015, -0.5509192354327178), (-0.34179695481150457, -0.5781411346850465), (-0.3327229883940617, -0.605363033937375), (-0.32364902197661893, -0.6325849331897035), (-0.3145750555591761, -0.6598068324420322), (-0.3055010891417333, -0.6870287316943607), (-0.29642712272429045, -0.7142506309466893), (-0.269205223471962, -0.7233245973641322), (-0.2510572906370764, -0.6961026981118036), (-0.23290935780219074, -0.668880798859475), (-0.20568745854986228, -0.6416588996071464), (-0.17846555929753383, -0.6144370003548179), (-0.1603176264626482, -0.5872151011024893), (-0.13309572721031973, -0.5599932018501607), (-0.1149477943754341, -0.5327713025978321), (-0.08772589512310566, -0.5055494033455036), (-0.060503995870777205, -0.4783275040931749), (-0.08772589512310566, -0.4692535376757321), (-0.12402176079287693, -0.4692535376757321), (-0.1603176264626482, -0.4692535376757321), (-0.19661349213241947, -0.4692535376757321), (-0.22383539138474792, -0.4783275040931749), (-0.2510572906370764, -0.48740147051061783), (-0.28735315630684766, -0.48740147051061783), (-0.3145750555591761, -0.5055494033455036), (-0.35087092122894736, -0.5055494033455036), (-0.3780928204812758, -0.5146233697629464), (-0.3780928204812758, -0.5509192354327178), (-0.35087092122894736, -0.5781411346850465), (-0.34179695481150457, -0.605363033937375), (-0.34179695481150457, -0.6416588996071464), (-0.34179695481150457, -0.6779547652769179), (-0.34179695481150457, -0.7142506309466893), (-0.34179695481150457, -0.7505464966164608), (-0.35087092122894736, -0.6961026981118036), (-0.369018854063833, -0.6325849331897035), (-0.3780928204812758, -0.5872151011024893), (-0.3780928204812758, -0.5509192354327178), (-0.3780928204812758, -0.5146233697629464), (-0.3780928204812758, -0.4783275040931749), (-0.3780928204812758, -0.4420316384234035), (-0.369018854063833, -0.41480973917107494), true], 1, (-2.6193625255896515, -3.9718045748086768), (6.137015067242667, 1.6994244360931117), (0, 625), (965, 0)) → stroke2
  25. AttachCopyToView(PolyLine[(-0.7047556115092173, -0.08814694814313193), (-0.6866076786743316, -0.11536884739546051), (-0.668459745839446, -0.1425907466477891), (-0.6321638801696747, -0.1425907466477891), (-0.6049419809173463, -0.15166471306523197), (-0.5777200816650178, -0.1607386794826748), (-0.5504981824126893, -0.17888661231756053), (-0.5232762831603609, -0.1879605787350034), (-0.4869804174905896, -0.1879605787350034), (-0.45068455182081835, -0.1879605787350034), (-0.4234626525684899, -0.19703454515244626), (-0.39624075331616143, -0.20610851156988913), (-0.4325366189859327, -0.19703454515244626), (-0.4597585182382612, -0.17888661231756053), (-0.4869804174905896, -0.1607386794826748), (-0.514202316742918, -0.1425907466477891), (-0.5414242159952465, -0.13351678023034624), true], 1, (-2.6193625255896515, -3.9718045748086768), (6.137015067242667, 1.6994244360931117), (0, 625), (965, 0)) → stroke3
  26. AttachCopyToView(PolyLine[(-0.5051283503254752, -1.3675762130025753), (-0.5051283503254752, -1.4129460450897897), (-0.5051283503254752, -1.449241910759561), (-0.5051283503254752, -1.4946117428467753), (-0.5051283503254752, -1.5399815749339896), (-0.4960543839080324, -1.5672034741863183), (-0.4869804174905896, -1.5944253734386469), (-0.47790645107314683, -1.6216472726909754), (-0.4325366189859327, -1.648869171943304), (-0.4053147197336043, -1.6579431383607468), (-0.35994488764639015, -1.648869171943304), (-0.34179695481150457, -1.6216472726909754), (-0.3145750555591761, -1.6034993398560897), (-0.29642712272429045, -1.5762774406037612), (-0.269205223471962, -1.5490555413514324), (-0.2510572906370764, -1.5218336420991039), (-0.23290935780219074, -1.4946117428467753), (-0.22383539138474792, -1.4673898435944468), (-0.2147614249673051, -1.4401679443421183), (-0.19661349213241947, -1.4673898435944468), (-0.19661349213241947, -1.5036857092642182), (-0.18753952571497665, -1.5309076085165467), (-0.18753952571497665, -1.5672034741863183), (-0.17846555929753383, -1.5944253734386469), (-0.17846555929753383, -1.6307212391084183), (-0.169391592880091, -1.585351407021204), (-0.1603176264626482, -1.5399815749339896), (-0.15124366004520537, -1.512759675681661), (-0.15124366004520537, -1.4764638100118896), (-0.14216969362776255, -1.449241910759561), (-0.169391592880091, -1.4401679443421183), (-0.20568745854986228, -1.449241910759561), (-0.24198332421963356, -1.4673898435944468), (-0.269205223471962, -1.4855377764293325), (-0.29642712272429045, -1.512759675681661), (-0.3327229883940617, -1.512759675681661), (-0.3780928204812758, -1.5218336420991039), (-0.41438868615104707, -1.5399815749339896), (-0.44161058540337556, -1.5309076085165467), (-0.44161058540337556, -1.4946117428467753), (-0.44161058540337556, -1.458315877177004), (-0.44161058540337556, -1.4220200115072326), (-0.4325366189859327, -1.385724145837461), (-0.4234626525684899, -1.3585022465851324), (-0.41438868615104707, -1.3312803473328039), (-0.4053147197336043, -1.3040584480804753), (-0.38716678689871864, -1.267762582410704), (-0.3780928204812758, -1.2314667167409323), (-0.39624075331616143, -1.2042448174886038), (-0.4053147197336043, -1.1770229182362753), (-0.4325366189859327, -1.1679489518188324), (-0.468832484655704, -1.1679489518188324), (-0.514202316742918, -1.1679489518188324), (-0.5504981824126893, -1.195170851071161), (-0.5958680144999035, -1.2405406831583752), (-0.6230899137522319, -1.267762582410704), (-0.6503118130045603, -1.3040584480804753), (-0.6775337122568887, -1.2949844816630325), (-0.6775337122568887, -1.2586886159932609), (-0.6775337122568887, -1.3040584480804753), (-0.6775337122568887, -1.3675762130025753), (-0.6866076786743316, -1.4220200115072326), (-0.6866076786743316, -1.458315877177004), (-0.6956816450917744, -1.5036857092642182), (-0.7047556115092173, -1.5309076085165467), (-0.71382957792666, -1.5581295077688755), (-0.7229035443441029, -1.5944253734386469), (-0.7319775107615457, -1.6579431383607468), (-0.7319775107615457, -1.6942390040305182), (-0.7319775107615457, -1.7305348697002898), (-0.7410514771789886, -1.7668307353700612), (-0.7410514771789886, -1.8031266010398326), (-0.7410514771789886, -1.7668307353700612), (-0.7410514771789886, -1.6942390040305182), (-0.7319775107615457, -1.6034993398560897), (-0.6866076786743316, -1.512759675681661), (-0.6866076786743316, -1.458315877177004), (-0.6775337122568887, -1.3947981122549038), (-0.668459745839446, -1.3585022465851324), (-0.6593857794220032, -1.385724145837461), (-0.6593857794220032, -1.4220200115072326), (-0.6956816450917744, -1.5036857092642182), (-0.7410514771789886, -1.5581295077688755), (-0.7864213092662026, -1.6579431383607468), (-0.8227171749359738, -1.7305348697002898), (-0.8499390741883023, -1.775904701787504), (-0.868087007023188, -1.8212745338747183), (-0.8862349398580736, -1.8575703995444899), (NaN, NaN), (-0.41438868615104707, -1.3947981122549038), (-0.3780928204812758, -1.4038720786723466), (-0.35087092122894736, -1.4220200115072326), (-0.32364902197661893, -1.4310939779246754), true], 1, (-2.6193625255896515, -3.9718045748086768), (6.137015067242667, 1.6994244360931117), (0, 625), (965, 0)) → stroke4
  27. AttachCopyToView(PolyLine[(-0.5323502495778037, -0.46017957125828923), (-0.5051283503254752, -0.4783275040931749), (-0.47790645107314683, -0.5055494033455036), (-0.45068455182081835, -0.5146233697629464), (-0.4234626525684899, -0.5327713025978321), (-0.39624075331616143, -0.541845269015275), (-0.35994488764639015, -0.5236973361803893), (-0.3145750555591761, -0.5055494033455036), (-0.28735315630684766, -0.48740147051061783), (-0.26013125705451917, -0.4783275040931749), (-0.22383539138474792, -0.4692535376757321), (-0.19661349213241947, -0.4511056048408464), (-0.169391592880091, -0.43295767200596064), (-0.14216969362776255, -0.4692535376757321), (-0.13309572721031973, -0.5236973361803893), (-0.13309572721031973, -0.5690671682676035), (-0.13309572721031973, -0.6144370003548179), (-0.13309572721031973, -0.6598068324420322), (-0.13309572721031973, -0.6961026981118036), (-0.13309572721031973, -0.7323985637815751), (-0.14216969362776255, -0.7596204630339036), (-0.15124366004520537, -0.7868423622862322), (-0.17846555929753383, -0.7596204630339036), (-0.18753952571497665, -0.7142506309466893), (-0.18753952571497665, -0.6598068324420322), (-0.18753952571497665, -0.6235109667722607), (-0.18753952571497665, -0.5872151011024893), (-0.17846555929753383, -0.5509192354327178), (-0.169391592880091, -0.5236973361803893), (-0.15124366004520537, -0.4964754369280607), (-0.14216969362776255, -0.4692535376757321), (-0.1149477943754341, -0.43295767200596064), (-0.09679986154054847, -0.40573577275363204), true], 1, (-2.6193625255896515, -3.9718045748086768), (6.137015067242667, 1.6994244360931117), (0, 625), (965, 0)) → stroke6
  28. AttachCopyToView(PolyLine[(1.9085467167143142, -0.12444281381290337), (1.9448425823840854, -0.12444281381290337), (1.9811384480538567, -0.12444281381290337), (2.017434313723628, -0.12444281381290337), (NaN, NaN), (3.4692689405144788, -0.11536884739546051), (3.50556480618425, -0.11536884739546051), (3.5418606718540215, -0.11536884739546051), (3.5781565375237925, -0.10629488097801765), (3.605378436776121, -0.08814694814313193), (3.6326003360284496, -0.07907298172568906), true], 1, (-2.6193625255896515, -3.9718045748086768), (6.137015067242667, 1.6994244360931117), (0, 625), (965, 0)) → stroke8
  29. AttachCopyToView(PolyLine[(6.3094204291740805, -0.08814694814313193), (6.354790261261295, -0.08814694814313193), (6.391086126931066, -0.08814694814313193), (6.418308026183395, -0.09722091456057479), (6.454603891853166, -0.09722091456057479), (6.499973723940379, -0.09722091456057479), (6.536269589610151, -0.09722091456057479), (6.572565455279922, -0.10629488097801765), (6.608861320949694, -0.10629488097801765), (6.645157186619465, -0.11536884739546051), (6.681453052289236, -0.11536884739546051), (6.717748917959008, -0.11536884739546051), (6.763118750046221, -0.11536884739546051), (6.7994146157159925, -0.12444281381290337), (6.835710481385764, -0.13351678023034624), (6.872006347055535, -0.1425907466477891), (6.899228246307864, -0.15166471306523197), (6.935524111977635, -0.1607386794826748), (6.980893944064849, -0.1698126459001177), (7.035337742569506, -0.17888661231756053), (7.08070757465672, -0.17888661231756053), (7.107929473909048, -0.1879605787350034), (7.1623732724137055, -0.1879605787350034), (7.189595171666034, -0.19703454515244626), (7.225891037335805, -0.19703454515244626), (7.27126086942302, -0.19703454515244626), (7.316630701510233, -0.19703454515244626), (7.362000533597447, -0.19703454515244626), (7.4073703656846615, -0.19703454515244626), (7.443666231354433, -0.19703454515244626), (7.479962097024204, -0.19703454515244626), (7.516257962693976, -0.19703454515244626), (7.552553828363747, -0.19703454515244626), (7.606997626868403, -0.19703454515244626), (7.634219526120732, -0.1879605787350034), (7.670515391790503, -0.1879605787350034), (7.72495919029516, -0.1698126459001177), (7.752181089547489, -0.1607386794826748), (7.779402988799817, -0.15166471306523197), (7.806624888052146, -0.1425907466477891), (7.842920753721917, -0.1425907466477891), (NaN, NaN), (6.336642328426409, -0.21518247798733198), (6.3729381940961805, -0.21518247798733198), (6.4273819926008375, -0.21518247798733198), (6.472751824688052, -0.21518247798733198), (6.509047690357822, 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-0.1607386794826748), (7.425518298519547, -0.1607386794826748), (7.470888130606761, -0.15166471306523197), (7.507183996276533, -0.15166471306523197), (7.552553828363747, -0.1425907466477891), (7.5888496940335175, -0.1425907466477891), (7.643293492538175, -0.1425907466477891), (7.688663324625389, -0.1425907466477891), (7.743107123130046, -0.1425907466477891), (7.779402988799817, -0.1425907466477891), (7.815698854469589, -0.1425907466477891), (7.870142652974245, -0.1425907466477891), (7.906438518644016, -0.1425907466477891), (NaN, NaN), (6.935524111977635, -0.09722091456057479), (6.971819977647407, -0.09722091456057479), (7.026263776152064, -0.09722091456057479), (7.071633608239277, -0.09722091456057479), (7.107929473909048, -0.09722091456057479), (7.1623732724137055, -0.09722091456057479), (7.2168170709183626, -0.09722091456057479), (7.253112936588134, -0.09722091456057479), (7.316630701510233, -0.09722091456057479), (7.352926567180004, -0.09722091456057479), (7.398296399267219, -0.08814694814313193), (7.43459226493699, -0.07907298172568906), (7.470888130606761, -0.07907298172568906), (7.5253319291114185, -0.07907298172568906), (7.570701761198633, -0.07907298172568906), (7.625145559703289, -0.07907298172568906), (7.66144142537306, -0.07907298172568906), (7.697737291042832, -0.07907298172568906), (7.752181089547489, -0.08814694814313193), (7.797550921634703, -0.09722091456057479), (7.833846787304474, -0.10629488097801765), (7.879216619391688, -0.11536884739546051), (7.915512485061459, -0.12444281381290337), (7.9518083507312305, -0.13351678023034624), (7.988104216401002, -0.13351678023034624), (8.01532611565333, -0.1425907466477891), (8.051621981323102, -0.1425907466477891), (8.087917846992873, -0.15166471306523197), (8.133287679080087, -0.15166471306523197), (8.169583544749859, -0.15166471306523197), (8.20587941041963, -0.15166471306523197), (8.260323208924286, -0.15166471306523197), (8.296619074594057, -0.15166471306523197), (8.323840973846385, -0.1607386794826748), (8.323840973846385, -0.19703454515244626), (8.314767007428943, -0.22425644440477485), (8.3056930410115, -0.26055231007454627), (8.278471141759171, -0.28777420932687486), (8.269397175341728, -0.31499610857920346), (8.260323208924286, -0.34221800783153206), (8.260323208924286, -0.38758783991874635), (8.260323208924286, -0.4238837055885178), (8.251249242506844, -0.4511056048408464), (NaN, NaN), (7.988104216401002, -0.31499610857920346), (7.779402988799817, -0.20610851156988913), (7.851994720139359, -0.20610851156988913), (7.906438518644016, -0.20610851156988913), (7.9518083507312305, -0.20610851156988913), (7.997178182818445, -0.19703454515244626), (8.042548014905659, -0.19703454515244626), (8.087917846992873, -0.19703454515244626), (8.124213712662645, -0.19703454515244626), (8.160509578332416, -0.19703454515244626), (8.196805444002187, -0.19703454515244626), (8.233101309671959, -0.19703454515244626), (8.269397175341728, -0.19703454515244626), (NaN, NaN), (7.879216619391688, -0.10629488097801765), (7.915512485061459, -0.10629488097801765), (7.960882317148673, -0.10629488097801765), (7.988104216401002, -0.09722091456057479), (8.024400082070773, -0.08814694814313193), (8.060695947740545, -0.08814694814313193), true], 1, (-2.6193625255896515, -4.271245466584291), (8.351062873098714, 1.6994244360931117), (0, 658), (1209, 0)) → stroke9
  30. AttachCopyToView(PolyLine[(0.22078896306995013, -0.24240437723966057), (0.2026410302350645, -0.21518247798733198), (0.17541913098273604, -0.20610851156988913), (0.15727119814785043, -0.17888661231756053), (0.13004929889552197, -0.1698126459001177), (0.10282739964319351, -0.15166471306523197), (0.09375343322575069, -0.12444281381290337), (NaN, NaN), (0.10282739964319351, -0.3512919742489749), (0.10282739964319351, -0.31499610857920346), (0.10282739964319351, -0.278700242909432), (0.10282739964319351, -0.24240437723966057), (0.10282739964319351, -0.20610851156988913), true], 1, (-2.6193625255896515, -4.271245466584291), (8.351062873098714, 1.6994244360931117), (0, 658), (1209, 0)) → stroke10
  31. Segment(O, D) → l
  32. Point(l) → F
  33. Segment(F, B) → m
  34. Point(l) → G
  35. Segment(F, G) → n