MathDB

6

Part of 2019 Cono Sur Olympiad

Problems(1)

2019 Cono Sur Mathematical Olympiad, P6

Source:

8/28/2019
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.
geometrycircumcircletangentorthocenter