MathDB
Problem 3

Source: Danube Mathematical Competition 2017, Romania

October 28, 2017
geometrycircumcircle

Problem Statement

Let O,HO,H be the circumcenter and the orthocenter of triangle ABCABC. Let FF be the foot of the perpendicular from C onto AB, and MM the midpoint of CHCH. Let N be the foot of the perpendicular from C onto the parallel through H at OMOM. Let DD be on ABAB such that CA=CDCA=CD. Let BNBN intersect CDCD at PP. Let PHPH intersect CACA at QQ. Prove that QF⊥OFQF\perp OF.
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