37 lines
1.2 KiB
Plaintext
37 lines
1.2 KiB
Plaintext
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根据题目要求，优先文本条件处理几何构造，忽略验证和标注命令。构造顺序：基本点→基础线段→圆→交点→派生点→多边形。输出严格遵循GeoGebra命令格式。
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```geo
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A = (3.2, 0)
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B = (0, 0)
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C = (0, 4.5)
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s_AB = Segment(A, B)
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s_BC = Segment(B, C)
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s_AC = Segment(A, C)
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D = Midpoint(B, C)
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E = Midpoint(A, C)
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F = Midpoint(A, B)
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s_AD = Segment(A, D)
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s_BE = Segment(B, E)
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s_CF = Segment(C, F)
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G = Intersect(s_AD, s_BE)
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c_BCF = Circle(B, C, F)
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c_ABE = Circle(A, B, E)
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l_BE = Line(B, E)
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l_AD = Line(A, D)
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P = Intersect(c_BCF, l_BE, 2)
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Q = Intersect(c_ABE, l_AD, 2)
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l_DP = Line(D, P)
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l_FQ = Line(F, Q)
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R = Intersect(l_DP, l_FQ)
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poly_ABC = Polygon(A, B, C)
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```
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说明：
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1. 使用图形提供的坐标定义基本点A、B、C
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2. 按顺序创建线段和中点（D、E、F为各边中点）
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3. 中线定义为线段（s_AD, s_BE, s_CF）
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4. 重心G通过中线交点得到
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5. 共圆条件转化为圆对象（c_BCF过B、C、F；c_ABE过A、B、E）
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6. P为圆BCF与直线BE的第二交点（排除B点），Q为圆ABE与直线AD的第二交点（排除A点）
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7. R定义为直线DP与FQ的交点
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8. 最终创建三角形ABC多边形
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