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ratio wanted related to orthocenter, circumcenter and 5 midpoints

Source: KJMO 2011 p5

May 3, 2019
ratiogeometrycircumcirclemidpointsmidpoint

Problem Statement

In triangle ABCABC, (AB≠ACAB \ne AC), let the orthocenter be HH, circumcenter be OO, and the midpoint of BCBC be MM. Let HM∩AO=DHM \cap AO = D. Let P,Q,R,SP,Q,R,S be the midpoints of AB,CD,AC,BDAB,CD,AC,BD. Let X=PQ∩RSX = PQ\cap RS. Find AH/OXAH/OX.
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