Let ABCD be a quadrilateral inscribed in a circle. If U is the intersection of its diagonals and V is the intersection of sides AB and CD, show that the tangents to the circle at A and at D meet line UV as the same point. Assume that neither of these tangents is parallel to UV. (Use cross ratios)

Question

Let ABCD be a quadrilateral inscribed in a circle.  If U is the intersection of its diagonals and V is the intersection of sides AB and CD, show that the tangents to the circle at A and at D meet line UV as the same point.  Assume that neither of these tangents is parallel to UV. (Use cross ratios)

anonymous · Answer

Here is the figure to go with the problem.