In the acute triangle ABC, ∠BAC is less than ∠ACB. Let AD be a diameter of ω, the circle circumscribed to said triangle. Let E be the point of intersection of the ray AC and the tangent to ω passing through B. The perpendicular to AD that passes through E intersects the circle circumscribed to the triangle BCE, again, at the point F. Show that CD is an angle bisector of ∠BCF. geometryangle bisectorcircumcircle