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Tangent and parallel lines

Source: Sharygin Geometry Olympiad 2012 - Problem 5

April 28, 2012
geometrycircumcircleratiocyclic quadrilateralgeometry unsolved

Problem Statement

On side ACAC of triangle ABCABC an arbitrary point is selected DD. The tangent in DD to the circumcircle of triangle BDCBDC meets ABAB in point C1C_{1}; point A1A_{1} is defined similarly. Prove that A1C1∥ACA_{1}C_{1}\parallel AC.
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