The area of the small circle p is πr*r * R * r.

The ratio of two areas is required, and the relationship between the radius of a large circle and the radius of a small circle is required. This topic investigates the tangent length theorem, pythagorean theorem,

Solution: Connect OP, PC, PE and PF.

So, the quadrangle OEPF is a square,

Let the radius of circle p be r, then op= R times the root sign.

O, P and C are on a straight line, so the sector radius R=PC+OP=r+ R twice the root sign.

The sector OAB area is 1/4 (πR*R).

The area of circle p is πr*r * R * r.

So the area ratio is (3+2 root number 2)/4.