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concurrency wanted, <APE =<BAC, <CQF = < BCA, orthocenter,

Source: Ukraine TST 2011 p10

May 5, 2020
concurrentconcurrencyequal anglesgeometryorthocenter

Problem Statement

Let H H be the point of intersection of the altitudes AP AP and CQ CQ of the acute-angled triangle ABCABC. The points E E and F F are marked on the median BM BM such that ∠APE=∠BAC \angle APE = \angle BAC , ∠CQF=∠BCA \angle CQF = \angle BCA , with point E E lying inside the triangle APBAPB and point F F is inside the triangle CQBCQB. Prove that the lines AE,CFAE, CF, and BHBH intersect at one point.
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