Problem

Source: IRAN 2017 2nd round p6

Tags: geometry, circumcircle



Let $ABC$ be a triangle and $X$ be a point on its circumcircle. $Q,P$ lie on a line $BC$ such that $XQ\perp AC , XP\perp AB$. Let $Y$ be the circumcenter of $\triangle XQP$. Prove that $ABC$ is equilateral triangle if and if only $Y$ moves on a circle when $X$ varies on the circumcircle of $ABC$.