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Prove that B'M is parallel to BC and AK is tangent (12)

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October 29, 2010
geometrygeometric transformationreflectiongeometry proposed

Problem Statement

Let ACAC be the greatest leg of a right triangle ABC,ABC, and CHCH be the altitude to its hypotenuse. The circle of radius CHCH centered at HH intersects ACAC in point M.M. Let a point B′B' be the reflection of BB with respect to the point H.H. The perpendicular to ABAB erected at B′B' meets the circle in a point KK. Prove that
a) B′M∥BCB'M \parallel BC
b) AKAK is tangent to the circle.
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