The circle ka touches the extensions of sides AB and BC, as well as the circumscribed circle of the triangle ABC (from the outside). We denote the intersection of ka with the circumscribed circle of the triangle ABC by A′. Analogously, we define points B′ and C′. Prove that the lines AA′,BB′ and CC′ intersect in one point. geometrycircumcircleconcurrencyconcurrenttangent circles