RMO 2014 Delhi Region Q.5

Let $ABC$ be an acute-angeled triangle and let $H$ be its orthocenter. For any point $P$ on the circumcircle of triangle $ABC$ , let $Q$ be the point of the intersection of the line $BH$ with the line $AP$ . Show that there is a unique point $X$ on the circumcircle of $ABC$ such that for every point $P\not=A,B$ the circumcircle of $HQP$ pass through $X$ .

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RMO 2014 Delhi Region Q.5

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