MathDB

Problem 6

Part of 2021 Pan-American Girls' Math Olympiad

Problems(1)

Incenter, Excenter and intersections

Source: Pan-American Girls’ Mathematical Olympiad 2021, P6

10/6/2021
Let ABCABC be a triangle with incenter II, and AA-excenter Γ\Gamma. Let A1,B1,C1A_1,B_1,C_1 be the points of tangency of Γ\Gamma with BC,ACBC,AC and ABAB, respectively. Suppose IA1,IB1IA_1, IB_1 and IC1IC_1 intersect Γ\Gamma for the second time at points A2,B2,C2A_2,B_2,C_2, respectively. MM is the midpoint of segment AA1AA_1. If the intersection of A1B1A_1B_1 and A2B2A_2B_2 is XX, and the intersection of A1C1A_1C_1 and A2C2A_2C_2 is YY, prove that MX=MYMX=MY.
geometryincenterexcenterPAGMO