computational, starting with intersecting circles
Source: December 2020 Ukraine Geometry Olympiad X p5 , XI p4
December 20, 2020
geometrycircles
Problem Statement
Let , be two circles, where has a smaller radius, intersect at two points and . Points lie on , respectively so that the point is the midpoint of the segment . Line intersects the circle for the second time at the point , line intersects the circle for the second time at the point . The perpendicular bisectors of the segments and intersect at a point . Knowing that and , find .