IMO 2007 Shortlist G2
Given an isosceles triangle ABC with AB = AC. The midpoint of side BC is denoted by M. Let X be a variable point on the ...
Category: Geometry
Problem
Given an isosceles triangle ABC with AB = AC. The midpoint of side BC is denoted by M. Let X be a variable point on the shorter arc MA of the circumcircle of triangle ABM. Let T be the point in the angle domain BMA, for which ∠TMX = 90◦ and TX = BX. Prove that ∠MTB − ∠CTM does not depend on X. (Canada)