MathDB
Geometry Proof

Source: ToT - 2001 Spring Junior A-Level #3

August 17, 2011
geometrygeometric transformationreflectionangle bisectorgeometry unsolved

Problem Statement

Point AA lies inside an angle with vertex MM. A ray issuing from point AA is reflected in one side of the angle at point BB, then in the other side at point CC and then returns back to point AA (the ordinary rule of reflection holds). Prove that the center of the circle circumscribed about triangle BCM\triangle BCM lies on line AMAM.