circumcenter of triangle BCD lies on the circumcircle of triangle ABC
Source: Kazakhstan NMO 2003 grade XI P6
May 12, 2019
geometrycircumcirclecircles
Problem Statement
Let the point lie on the circle and let the point , other than the point , lie on the tangent to the circle passing through the point . Let a point be chosen outside the circle , so that the segment intersects at two different points. Let the circle touch the line at the point and the circle at the point , on the opposite side from the point with respect to the line . Prove that the center of the circumcircle of triangle lies on the circumcircle of triangle .