There are two main approaches to solving this problem. The following hint describes the intended solution path, though interestingly, most successful submissions used an alternative method.
Consider the following construction:
- Draw a circle with center O
- Choose a point P outside the circle
- Draw a line s through both P and O
- Label as A the intersection point of line s with the circle that is farther from P
- Draw two tangent lines: one tangent t through point A, and another tangent through point P, labeling its point of tangency as T
What appears to be useful for the constructions is that the angle between lines AT and PT is equal to the angle between tangent t and line AT. (This crucial fact requires proof!)
Please submit the solution to this problem via e-mail to physcs.cup@gmail.com.