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concurrency wanted, 2 circumcircles and tangents related

Source: 2011 Oral Moscow Geometry Olympiad grades 10-11 p6

April 7, 2020
geometrycircumcirclealtitudesconcurrencyconcurrent

Problem Statement

Let AA1,BB1AA_1 , BB_1, and CC1CC_1 be the altitudes of the non-isosceles acute-angled triangle ABCABC. The circles circumscibred around the triangles ABCABC and A1B1CA_1 B_1 C intersect again at the point P,ZP , Z is the intersection point of the tangents to the circumscribed circle of the triangle ABCABC conducted at points AA and BB . Prove that lines AP,BCAP , BC and ZC1ZC_1 are concurrent.
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