Balkan Mathematical Olympiad 2018 P1
Source: BMO 2018
May 9, 2018
Problem Statement
A quadrilateral is inscribed in a circle where ,and is not paralel to .Point is the intersection of diagonals and , and the perpendicular from to intersects the segment at a point .If bisects the angle prove that is diameter of .
Proposed by Emil Stoyanov,Bulgaria