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Show that EX is parallel with AP

Source: Iran Pre-Preparation Course Examination 1997, E1, P5

March 8, 2010
geometrycircumcircleparallelogramrotationgeometry unsolved

Problem Statement

Let HH be the orthocenter of the triangle ABCABC and PP an arbitrary point on circumcircle of triangle. BHBH meets ACAC at EE. PAQBPAQB and PARCPARC are two parallelograms and AQAQ meets HRHR at XX. Show that EX∥APEX \parallel AP.
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