IMO Shortlist 2007 problem G2

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Dodao/la: arhiva
April 2, 2012
Denote by M midpoint of side BC in an isosceles triangle \triangle ABC with AC = AB. Take a point X on a smaller arc \widehat{MA} of circumcircle of triangle \triangle ABM. Denote by T point inside of angle BMA such that \angle TMX = 90 and TX = BX.

Prove that \angle MTB - \angle CTM does not depend on choice of X.

Author: unknown author, Canada
Source: Međunarodna matematička olimpijada, shortlist 2007