MathDB
BD //AC , reflections of touchpoints of incircle wrt lines

Source: Sharygin Finals 2022 8.5

October 26, 2022
geometrygeometric transformationreflection

Problem Statement

An incircle of triangle ABCABC touches ABAB, BCBC, ACAC at points C1C_1, A1A_1,B1 B_1 respectively. Let AA' be the reflection of A1A_1 about B1C1B_1C_1, point CC' is defined similarly. Lines AC1A'C_1 and CA1C'A_1 meet at point DD. Prove that BDACBD \parallel AC.