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P13 [Geometry] - Turkish NMO 1st Round - 2014

Source:

May 23, 2014
geometry

Problem Statement

Let ABCDABCD be a convex quadrilateral such that m(ADB^)=15∘m \left (\widehat{ADB} \right)=15^{\circ}, m(BCD^)=90∘m \left (\widehat{BCD} \right)=90^{\circ}. The diagonals of quadrilateral are perpendicular at EE. Let PP be a point on ∣AE∣|AE| such that ∣EC∣=4,∣EA∣=8|EC|=4, |EA|=8 and ∣EP∣=2|EP|=2. What is m(PBD^)m \left (\widehat{PBD} \right)?
<spanclass=′latex−bold′>(A)</span> 15∘<spanclass=′latex−bold′>(B)</span> 30∘<spanclass=′latex−bold′>(C)</span> 45∘<spanclass=′latex−bold′>(D)</span> 60∘<spanclass=′latex−bold′>(E)</span> 75∘ <span class='latex-bold'>(A)</span>\ 15^{\circ} \qquad<span class='latex-bold'>(B)</span>\ 30^{\circ} \qquad<span class='latex-bold'>(C)</span>\ 45^{\circ} \qquad<span class='latex-bold'>(D)</span>\ 60^{\circ} \qquad<span class='latex-bold'>(E)</span>\ 75^{\circ}
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