Problem

Source: 2022 Taiwan TST Round 1 Mock Day 2 P5

Tags: geometry, circumcircle, Taiwan



Let H be the orthocenter of a given triangle ABC. Let BH and AC meet at a point E, and CH and AB meet at F. Suppose that X is a point on the line BC. Also suppose that the circumcircle of triangle BEX and the line AB intersect again at Y, and the circumcircle of triangle CFX and the line AC intersect again at Z. Show that the circumcircle of triangle AYZ is tangent to the line AH. Proposed by usjl