The incircle of △ABC tangents BC, CA, AB at D, E, F, respectively. The projections of B, C to AD are U, V, respectively; the projections of C, A to BE are W, X, respectively; and the projections of A, B to CF are Y, Z, respectively. Show that the circumcircle of the triangle formed by UX, VY, WZ is tangent to the incircle of △ABC. geometryincircletangent circlescircumcircle