MathDB

3

Part of 2014 Taiwan TST Round 3

Problems(1)

TS sweep: Circle MX1X2 passes through mixtilinear touchpoint

Source: Taiwan 2014 TST3, Problem 3

7/18/2014
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.
geometrycircumcircleincentergeometric transformationhomothetyratioparallelogram