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22

Part of 2012 Sharygin Geometry Olympiad

Problems(1)

Circle inscribed between an arc and a chord

Source: Sharygin Geometry Olympiad 2012 - Problem 22

4/28/2012
A circle ω\omega with center II is inscribed into a segment of the disk, formed by an arc and a chord ABAB. Point MM is the midpoint of this arc ABAB, and point NN is the midpoint of the complementary arc. The tangents from NN touch ω\omega in points CC and DD. The opposite sidelines ACAC and BDBD of quadrilateral ABCDABCD meet in point XX, and the diagonals of ABCDABCD meet in point YY. Prove that points X,Y,IX, Y, I and MM are collinear.
geometrycircumcirclecyclic quadrilateralangle bisectorSharygin Geometry Olympiad