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2019 Cono Sur Mathematical Olympiad, P6

Source:

August 28, 2019
geometrycircumcircletangentorthocenter

Problem Statement

Let ABCABC be an acute-angled triangle with AB<ACAB< AC, and let HH be its orthocenter. The circumference with diameter AHAH meets the circumscribed circumference of ABCABC at P≠AP\neq A. The tangent to the circumscribed circumference of ABCABC through PP intersects line BCBC at QQ. Show that QP=QHQP=QH.
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