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P,Q on AB,CD maximising the (equal) angles CPD,BQA

Source: Baltic Way 1996 Q4

March 19, 2011
geometrytrapezoidgeometry proposed

Problem Statement

ABCDABCD is a trapezium where AD∥BCAD\parallel BC. PP is the point on the line ABAB such that ∠CPD\angle CPD is maximal. QQ is the point on the line CDCD such that ∠BQA\angle BQA is maximal. Given that PP lies on the segment ABAB, prove that ∠CPD=∠BQA\angle CPD=\angle BQA.
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