Question

State a definition for a polygon inscribed in a sphere.

Answer 1

Consider the situation given below:

Let a regular polygon be inscribed in a sphere such that its circumcentre is at a distance r from the centre of the sphere of radius R. A point source of light is kept at the centre of the sphere. How can we calculate the area of the shadow made on the surface of the sphere.

I tried to use the relation: Ω=SR2

But of course that is the case when a circle would be inscribed. So can I somehow relate it for any general polygon?