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Scalene Triangle with Incentre

Source: All Russian Olympiad 2015 11.7

December 11, 2015
incenterincirclegeometry

Problem Statement

A scalene triangle ABCABC is inscribed within circle ω\omega. The tangent to the circle at point CC intersects line ABAB at point DD. Let II be the center of the circle inscribed within △ABC\triangle ABC. Lines AIAI and BIBI intersect the bisector of ∠CDB\angle CDB in points QQ and PP, respectively. Let MM be the midpoint of QPQP. Prove that MIMI passes through the middle of arc ACBACB of circle ω\omega.
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