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prove that the orthocenter of one triangle lies on the circumcircle of another

Source: 2012 Sharygin Geometry Olympiad Final Round 8.6

August 3, 2018
geometrycircumcircleorthocenter

Problem Statement

Let ω\omega be the circumcircle of triangle ABCABC. A point B1B_1 is chosen on the prolongation of side ABAB beyond point B so that AB1=ACAB_1 = AC. The angle bisector of ∠BAC\angle BAC meets ω\omega again at point WW. Prove that the orthocenter of triangle AWB1AWB_1 lies on ω\omega .
(A.Tumanyan)
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