MathDB

6

Part of 2007 Chile National Olympiad

Problems(1)

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

Source: Chile 2007 L2 p6

5/26/2019
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.
geometryanglesAngle Chasingcircumcircle