Let the point D lie on the arc AC of the circumcircle of the triangle ABC (AB<BC), which does not contain the point B. On the side AC are selected an arbitrary point X and a point X′ for which ∠ABX=∠CBX′. Prove that regardless of the choice of the point X, the circle circumscribed around △DXX′, passes through a fixed point, which is different from point D.(Nikolaev Arseniy) geometrycircumcirclefixedFixed pointequal angles