完全四边形与圆的构造
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本范例展示了通过完全四边形的交点和中点构造的三个圆。它涉及几何作图的核心概念,包括线、交点、中点和圆的构造。使用了GeoGebra中的Line, Intersect, Segment, Midpoint, Circle等命令。适合初中及以上学生学习几何作图和圆的相关性质。
GeoGebra 命令及参数
Line(D, A) → fLine(A, C) → gLine(C, B) → hLine(B, A) → iLine(D, C) → jLine(D, B) → kIntersect(f, h) → I_{AD∧BC}Intersect(k, g) → I_{AC∧BD}Intersect(j, i) → I_{AB∧CD}Segment(A, B) → rSegment(A, I_{AC∧BD}) → nSegment(B, I_{AD∧BC}) → pMidpoint(A, D) → M_{AD}Midpoint(D, B) → M_{BD}Midpoint(C, D) → M_{CD}Midpoint(A, B) → M_{AB}Midpoint(A, C) → M_{AC}Midpoint(C, B) → M_{BC}Segment(D, B) → mSegment(B, I_{AC∧BD}) → sSegment(D, A) → lSegment(D, C) → qSegment(C, I_{AB∧CD}) → aCircle(I_{AD∧BC}, M_{AD}, M_{BC}) → cCircle(I_{AC∧BD}, M_{BD}, M_{AC}) → dCircle(I_{AB∧CD}, M_{AB}, M_{CD}) → eSegment(I_{AC∧BD}, C) → bSegment(C, I_{AD∧BC}) → f_1Segment(A, I_{AB∧CD}) → tSegment(A, I_{AD∧BC}) → h_1Conic(M_{BD}, M_{BC}, M_{AC}, M_{AD}, I_{AB∧CD}) → p9Intersect(d, c) → I_{dc}1, I_{dc}2, ,Line(I_{dc}1, I_{dc}2) → Rx_{dc}Intersect(e, c) → I_{ec}1, I_{ec}2, ,Line(I_{ec}1, I_{ec}2) → Rx_{ec}Intersect(e, d) → I_{ed}1, I_{ed}2, ,Line(I_{ed}2, I_{ed}1) → Rx_{ed}Intersect(Rx_{ed}, Rx_{dc}) → Rc