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Source: SMO(O) 2014 #2

January 22, 2015
geometry

Problem Statement

Let ABCABC be an acute-angled triangle and let DD, EE, and FF be the midpoints of BCBC, CACA, and ABAB respectively. Construct a circle, centered at the orthocenter of triangle ABCABC, such that triangle ABCABC lies in the interior of the circle. Extend EFEF to intersect the circle at PP, FDFD to intersect the circle at QQ and DEDE to intersect the circle at RR. Show that AP=BQ=CRAP=BQ=CR.
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