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<MTB - <CTM does not depend on X, where X lies on circumcircle

Source: Chile 2007 L2 p6

May 26, 2019
geometryanglesAngle Chasingcircumcircle

Problem Statement

Given an △ABC\triangle ABC isoceles with base BCBC we note with MM the midpoint of said base. Let XX be any point on the shortest arc AMAM of the circumcircle of △ABM\triangle ABM and let TT be a point on the inside ∠BMA\angle BMA such that ∠TMX=90o\angle TMX = 90^o and TX=BXTX = BX. Show that ∠MTB−∠CTM\angle MTB - \angle CTM does not depend on XX.
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