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four points lie on a circle

Source: China south east mathematical olympiad 2008 day1 problem 3

July 14, 2013
geometrycircumcircleperpendicular bisectorgeometry unsolved

Problem Statement

In △ABC\triangle ABC, side BC>ABBC>AB. Point DD lies on side ACAC such that ∠ABD=∠CBD\angle ABD=\angle CBD. Points Q,PQ,P lie on line BDBD such that AQ⊥BDAQ\bot BD and CP⊥BDCP\bot BD. M,EM,E are the midpoints of side ACAC and BCBC respectively. Circle OO is the circumcircle of △PQM\triangle PQM intersecting side ACAC at HH. Prove that O,H,E,MO,H,E,M lie on a circle.
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