Let be a quadrilateral inscribed in a circle Let the tangent to at meet rays and at and respectively. A point is chosen inside so that and Let be a point on segment satisfying Prove that lines and are concurrent.
In the triangle let be the foot of the altitude from to the side and ,, be the incenter, -excenter, and -excenter, respectively. Denote by and the other intersection points of the circle with the lines and , respectively. Prove that .