Problem 5
Let ABCD be a quadrilateral inscribed in a circle omega, and let P be a point on the extension of AC such that PB and PD are tangent to omega. The tangent at C intersects PD at Q and the line AD at R. Let E be the second point of intersection of AQ and omega. Prove that B, E, R are collinear.
Step 1 of 7: Reduce to equality of intersections
Detailed analysis
The desired collinearity is equivalent to showing that the point R where CQ meets AD is also the point where BE meets AD. Define that latter point as R'.