ABCD is cyclic if angles are equal, incircles related
Source: Indian Postal Coaching 2008 set 5 p5
May 25, 2020
geometryincirclecyclic quadrilateralanglesequal angles
Problem Statement
A convex quadrilateral is given. There rays and meet in , and the rays and meet in . Let be the projection of on . Prove that is cyclic if and only if the angle between the rays beginning at and tangent to the incircle of triangle is equal to the angle between the rays beginning at and tangent to the incircle of triangle . Also fi nd out whether is inscribable or circumscribable and justify.