# Inside an icosahedron

Geometry Level pending

Points A and B are chosen uniformly at random inside two regular icosahedra of edge lengths 2 and 20 respectively, both centered at the origin. (i.e. Point A is in the smaller one and B in the larger one.)

What is the probability that the distance between A and B is less than 5?

Useful formula: $$V_{icosahedron} = \frac{5(3+\sqrt5)}{12} a^3$$ where $$a =$$ Edge length