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Prove that I,J,P,H are concyclic

Source: Iran TST 2013: TST 1, Day 1, Problem 1

April 17, 2013
geometryincentertrigonometrycyclic quadrilateralgeometry proposed

Problem Statement

In acute-angled triangle ABCABC, let HH be the foot of perpendicular from AA to BCBC and also suppose that JJ and II are excenters oposite to the side AHAH in triangles ABHABH and ACHACH. If PP is the point that incircle touches BCBC, prove that I,J,P,HI,J,P,H are concyclic.
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