MathDB
fixed length for AK, common ext. tangent of incircles of ABD, ACD

Source: TOT 416 1994 Spring A S4 - Tournament of Towns

June 12, 2024
geometryfixed

Problem Statement

A point DD is placed on the side BC BC of the triangle ABCABC. Circles are inscribed in the triangles ABDABD and ACDACD, their common exterior tangent line (other than BCBC) intersects ADAD at the point KK. Prove that the length of AKAK does not depend on the position of DD. (An exterior tangent of two circles is one which is tangent to both circles but does not pass between them.)
(I Sharygin)