MEMO 2011 pojedinačno problem 3
In a plane the circles and with centers and , respectively, intersect in two points and . Assume that is obtuse. The tangent to in intersects again in and the tangent to in intersects again in . Let be the circumcircle of the triangle . Let be the midpoint of that arc of that contains . The lines and intersect again in and , respectively. Prove that the line is perpendicular to .