MathDB
2013-2014 Fall OMO #10

Source:

October 30, 2013
Online Math Opengeometrycircumcirclepower of a point

Problem Statement

In convex quadrilateral AEBCAEBC, ∠BEA=∠CAE=90∘\angle BEA = \angle CAE = 90^{\circ} and AB=15AB = 15, BC=14BC = 14 and CA=13CA = 13. Let DD be the foot of the altitude from CC to AB‾\overline{AB}. If ray CDCD meets AE‾\overline{AE} at FF, compute AE⋅AFAE \cdot AF.
Proposed by David Stoner
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