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Prove that < EMK = 90

Source: Tournament of Towns Spring 2003 - Senior A-Level - Problem 4

June 15, 2011
geometrygeometry proposed

Problem Statement

A right triangle ABCABC with hypotenuse ABAB is inscribed in a circle. Let KK be the midpoint of the arc BCBC not containing A,NA, N the midpoint of side ACAC, and MM a point of intersection of ray KNKN with the circle. Let EE be a point of intersection of tangents to the circle at points AA and CC. Prove that ∠EMK=90∘\angle EMK = 90^\circ.
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