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. The rocket cuts the atmospheric layer at point A, grazes the planet P1 and goes out of the atmospheric layer at point B. If AB = 100 km, what is the area of cross section of the atmospheric layer?
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
Questions, answers, comments welcome