PQ bisects I_CL, excircle related, CD=r_c 2021 Kharkiv City MO 11.4
Source:
December 29, 2021
geometryexcirclebisects segmentexcenter
Problem Statement
In the triangle , the segment is the angle bisector. The -exscribed circle with center at the point touches the side of the at the point and the extension of sides and at points and , respectively. It turned out that the length of the segment is equal to the radius of this exscribed circle. Prove that the line bisects the segment .