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2 intersection points of tangents and incenter of ABCD are collinear

Source: Sharygin Geometry Olympiad 2014 Correspondence Round P18

August 1, 2018
geometrycircumcircleincenter

Problem Statement

Let II be the incenter of a circumscribed quadrilateral ABCDABCD. The tangents to circle AICAIC at points A,CA, C meet at point XX. The tangents to circle BIDBID at points B,DB, D meet at point YY . Prove that X,I,YX, I, Y are collinear.
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