# Four is a crowd

Discrete Mathematics Level pending

Three points are chosen uniformly at random within a unit circle in the $$xy$$-plane.

A fourth point is chosen uniformly at random on the perimeter of a circle with radius $$r$$.

For $$r >> 1$$, (say $$r \approx 1,000,000,000$$), what does the probability $$p$$ that the four points form a convex quadrilateral approach?

×