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ABCD is cyclic with BC=CD

Source: Czech - Polish - Slovak Match 2013: P1

May 24, 2014
geometrygeometric transformationhomothetyLaTeXcyclic quadrilateralgeometry unsolved

Problem Statement

Suppose ABCDABCD is a cyclic quadrilateral with BC=CDBC = CD. Let ω\omega be the circle with center CC tangential to the side BDBD. Let II be the centre of the incircle of triangle ABDABD. Prove that the straight line passing through II, which is parallel to ABAB, touches the circle ω\omega.
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