collinear wanted, starting with a cyclic ABCD, incircle , excircle related
Source: Ukraine TST 2010 p2
May 4, 2020
geometrycyclic quadrilateralcollinearincircleexcircle
Problem Statement
Let be a quadrilateral inscribled in a circle with the center be the point of intersection of the diagonals and , . Rays and intersect at the point . The circle with center inscribed in the triangle touches at point . The -excircle with center in the triangle touches the side at the point T. Line and intersect at . Prove that the points , and lie on a straight line.