MathDB
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 ABCABC, the segment CLCL is the angle bisector. The CC-exscribed circle with center at the point Ic I_c touches the side of the ABAB at the point DD and the extension of sides CACA and CBCB at points PP and QQ, respectively. It turned out that the length of the segment CDCD is equal to the radius of this exscribed circle. Prove that the line PQPQ bisects the segment ICLI_CL.