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Symmedian passes through intersection of two circumcircle

Source: Sharygin Geometry Olympiad Correspondence Round 2017 P-12 (Grade-9-10)

May 1, 2017
geometrycircumcircle

Problem Statement

Let AA1,CC1AA_1 , CC_1 be the altitudes of triangle ABC,B0ABC, B_0 the common point of the altitude from BB and the circumcircle of ABCABC; and QQ the common point of the circumcircles of ABCABC and A1C1B0A_1C_1B_0, distinct from B0B_0. Prove that BQBQ is the symmedian of ABCABC. Proposed by D.Shvetsov
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