MathDB
Easy Geometry in Taiwan TST

Source: 2020 Taiwan TST Round 3

May 22, 2020
geometryexcircle

Problem Statement

Let Ω\Omega be the AA-excircle of triangle ABCABC, and suppose that Ω\Omega is tangent to lines BCBC, CACA, and ABAB at points DD, EE, and FF, respectively. Let MM be the midpoint of segment EFEF. Two more points PP and QQ are on Ω\Omega such that EPEP and FQFQ are both parallel to DMDM. Let BPBP meet CQCQ at point XX. Prove that the line AMAM is the angle bisector of ∠XAD\angle XAD.
Proposed by Shuang-Yen Lee
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