tiwe0/geochat/geometric-construction

Claude Code and agent skill by tiwe0/geochat

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尺规作图、垂直平分线、角平分线、作圆、作切线和作图依据说明技能。

Install

npx vskill@latest install tiwe0/geochat/geometric-construction

SKILL.md

尺规作图

适用于要求作图步骤、轨迹依据或只允许直尺圆规基本构造的题目。若题目允许直接使用变换命令且重点是对应关系,使用 geometric-transformations;不要用坐标计算或测量后回填数值冒充尺规构造。

构造规则

  1. 明确给定对象、允许操作和目标对象,每一步对应画圆/圆弧、作直线或取交点。
  2. 先创建被引用对象;交点、平分线和切点必须保留依赖,不能按当前图形手工放置。
  3. 对有两个交点或两个解的步骤说明分支选择;隐藏辅助对象前先保留可复核的依据。
  4. 验证等距、垂直或等角性质,并检查给定点重合、圆不相交、切点合并等退化情形。

小型原生例子:作线段垂直平分线

例子独立;执行前先确认名称无冲突,再按行输入。

ggb
A = (-2, 0)
B = (2, 0)
cA = Circle(A, B)
cB = Circle(B, A)
C = Intersect(cA, cB, 1)
D = Intersect(cA, cB, 2)
bisector = Line(C, D)
M = Intersect(bisector, Line(A, B))
equalCheck = Distance(M, A) == Distance(M, B)
perpendicularCheck = ArePerpendicular(bisector, Line(A, B))

预期:M = (0, 0),两个检查均为 true;移动 A 或 B 后,圆、交点和平分线同步更新。正常检查任意不同端点;边界检查端点非常接近时构造仍依赖两端点;退化检查 A = B 时两圆重合、交点和垂直平分线不唯一,不能伪造结果。

结果边界

“构造看起来正确”不等于依据正确。若某条命令或参数形态不确定,先用 searchGeoGebraCommands 核对;只使用原生命令,不用 JavaScript、XML 或 Execute 拼接步骤。

官方参考:Circle、Intersect、PerpendicularBisector、AngleBisector。

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