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TS sweep: Circle MX1X2 passes through mixtilinear touchpoint

Source: Taiwan 2014 TST3, Problem 3

July 18, 2014
geometrycircumcircleincentergeometric transformationhomothetyratioparallelogram

Problem Statement

Let MM be any point on the circumcircle of triangle ABCABC. Suppose the tangents from MM to the incircle meet BCBC at two points X1X_1 and X2X_2. Prove that the circumcircle of triangle MX1X2MX_1X_2 intersects the circumcircle of ABCABC again at the tangency point of the AA-mixtilinear incircle.
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