MathDB
AMC right angle

Source: oliforum contest, round 1, problem 2

September 21, 2008
vectorgeometrycircumcirclegeometric transformationreflectionparallelogramtrapezoid

Problem Statement

Let ABCD ABCD be a cyclic quadrilateral with AB>CD AB>CD and BC>AD BC>AD. Take points X X and Y Y on the sides AB AB and BC BC, respectively, so that AX\equal{}CD and AD\equal{}CY. Let M M be the midpoint of XY XY. Prove that AMC AMC is a right angle.
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