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equal segments related to AC and tangents of circumcircles of CHB,AHB

Source: 2011 Sharygin Geometry Olympiad Correspondence Round P9

April 2, 2019
geometryorthocenterTangentsequal segments

Problem Statement

Let HH be the orthocenter of triangle ABCABC. The tangents to the circumcircles of triangles CHBCHB and AHBAHB at point HH meet ACAC at points A1A_1 and C1C_1 respectively. Prove that A1H=C1HA_1H = C_1H.
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