Let O be the circumcircle of a triangle ABC. Let w be the

Last updated: 7/10/2022

Let O be the circumcircle of a triangle ABC. Let w be the circle tangent to BC, CA, AB at points D, E, F, respectively, such that A and w are on different sides of BC. Prove that if the radiuses of the circumcircle of the triangle ABC and w are equal, then the line OD is perpendicular to the line EF.