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Equal angles with a point on altitude

Source: RMM 2018 SL G1

February 21, 2019
geometrycircumcircle

Problem Statement

Let ABCABC be a triangle and let HH be the orthogonal projection of AA on the line BCBC. Let KK be a point on the segment AHAH such that AH=3KHAH = 3 KH. Let OO be the circumcenter of triangle ABCABC and let MM and NN be the midpoints of sides ACAC and ABAB respectively. The lines KOKO and MNMN meet at a point ZZ and the perpendicular at ZZ to OKOK meets lines AB,ACAB, AC at XX and YY respectively. Show that ∠XKY=∠CKB\angle XKY = \angle CKB.
Italy
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