斯库顿定理巧解几何问题

Scudon’s Theorem Cleverly Solves Geometric Problems

摘要: 角平分线是平面几何的基本元素之一，其相关线段长度的求解在高考和强基计划考试中不乏其身影，此类题目计算量大且过程繁琐。而斯库顿定理(也被称为角平分线长定理)，其核心表达式直接建立了角平分线和三角形三边的量化关系，可为这类问题的计算提供高效简化的解题路径。

Abstract: The angle bisector is one of the fundamental elements of plane geometry, and the calculation of the lengths of related line segments frequently appears in the Gaokao and the Strong Foundation Plan exams. These types of problems involve large amounts of calculation and complex processes. The Stewart’s theorem (also known as the Angle Bisector Length Theorem), directly establishes a quantitative relationship between the angle bisector and the three sides of the triangle, which can provide an efficient and simplified solution path for such problems.