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Parallel

Source: All Russian Mathematical Olympiad 2008. 10.6

June 13, 2008
geometrycircumcirclegeometric transformationreflectiontrigonometrygeometry proposed

Problem Statement

In a scalene triangle ABC ABC the altitudes AA1 AA_{1} and CC1 CC_{1} intersect at H,O H, O is the circumcenter, and B0 B_{0} the midpoint of side AC AC. The line BO BO intersects side AC AC at P P, while the lines BH BH and A1C1 A_{1}C_{1} meet at Q Q. Prove that the lines HB0 HB_{0} and PQ PQ are parallel.
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