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Chasing After the Tangent

Source: 2022 Taiwan TST Round 1 Mock Day 2 P5

March 19, 2022
geometrycircumcircleTaiwan

Problem Statement

Let HH be the orthocenter of a given triangle ABCABC. Let BHBH and ACAC meet at a point EE, and CHCH and ABAB meet at FF. Suppose that XX is a point on the line BCBC. Also suppose that the circumcircle of triangle BEXBEX and the line ABAB intersect again at YY, and the circumcircle of triangle CFXCFX and the line ACAC intersect again at ZZ. Show that the circumcircle of triangle AYZAYZ is tangent to the line AHAH.
Proposed by usjl
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