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An easy geometry from iran

Source: IRAN 2017 2nd round p6

April 21, 2017
geometrycircumcircle

Problem Statement

Let ABCABC be a triangle and XX be a point on its circumcircle. Q,PQ,P lie on a line BCBC such that XQ⊥AC,XP⊥ABXQ\perp AC , XP\perp AB. Let YY be the circumcenter of △XQP\triangle XQP. Prove that ABCABC is equilateral triangle if and if only YY moves on a circle when XX varies on the circumcircle of ABCABC.
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