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concurrent starting with an inscribed ABCD and tangents from a point on AC

Source: 2014 IMAC Arhimede P2

May 2, 2019
geometryconcurrentconcurrencytangential quadrilateralTangents

Problem Statement

A convex quadrilateral ABCDABCD is inscribed into a circle ω\omega . Suppose that there is a point XX on the segment ACAC such that the XBXB and XDXD tangents to the circle ω\omega . Tangent of ω\omega at CC, intersect XDXD at QQ. Let EE (E≠AE\ne A) be the intersection of the line AQAQ with ω\omega . Prove that AD,BEAD, BE, and CQCQ are concurrent.
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