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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