problem solving - planet circles

Consider a planet P1(like earth) that is spherical in shape. It has an atmospheric layer around it that also takes the same shape as that of the planet. An adventurist launches a rocket from a neighboring planet P2 to this planet P1, cuts the atmospheric layer at point A, grazes the planet P1 and goes out of the atmospheric layer at point B. If AB = 100kms, what is the area of cross section of the atmospheric layer?

 Explanation:

 Consider the following diagram.

The question essentially boils down to a case where a chord AB to the outer circle is a tangent to the inner circle. We have to find out the area between the two circles.

Therefore, Required Area = Area of outer circle - Area of inner circle
                                      = pi*(502 + r2) - pi*r2
                                                   = 2500*pi