2012 JBMO Problems/Problem 2
Let the circles and intersect at two points and , and let be a common tangent of and that touches and at and respectively. If and , evaluate the angle .
Let and be the centers of circles and respectively. Also let be the intersection of and line .
Note that is perpendicular to since is a tangent of . In order for to be perpendicular to , must be the point diametrically opposite . (to be continued.)