tangency implying cyclic quadrilateral
Source: 2021 Iran second round mathematical Olympiad P3
May 15, 2021
geometrycircumcirclecyclic quadrilateral
Problem Statement
Circle is inscribed in quadrilateral and is tangent to segments at , respectively. intersects for the second time at . if the circumcircle of triangle is tangent to lines and , prove that quadrilateral is cyclic.