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another sum PQ+PE+QF inside a right triangle (2011 HOMC Junior Q10)

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July 18, 2019
geometryright triangles

Problem Statement

Consider a right -angle triangle ABCABC with A=90oA=90^{o}, AB=cAB=c and AC=bAC=b. Let P∈ACP\in AC and Q∈ABQ\in AB such that ∠APQ=∠ABC\angle APQ=\angle ABC and ∠AQP=∠ACB\angle AQP = \angle ACB. Calculate PQ+PE+QFPQ+PE+QF, where EE and FF are the projections of BB and QQ onto BCBC, respectively.
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