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All-Russian Olympiad Day 1 Problem 10.2.

Source: All-Russian Olympiad 2018

April 24, 2018
geometry

Problem Statement

Let △ABC\triangle ABC be an acute-angled triangle with AB<ACAB<AC. Let MM and NN be the midpoints of ABAB and ACAC, respectively; let ADAD be an altitude in this triangle. A point KK is chosen on the segment MNMN so that BK=CKBK=CK. The ray KDKD meets the circumcircle Ω\Omega of ABCABC at QQ. Prove that C,N,K,QC, N, K, Q are concyclic.
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