You have 2 concentric circles of different radius (r for the small circle, R for the big circle), and a tangent to the small circle.
You have to find out the pink area. Come up with a general formula for any given r (small circle radius) and R (big circle radius).
Good luck! NO CALCULUS ALLOWED! ;)
Call one-half the length of the dark red line L. Since a tangent line is always perpendicular to the radius, this forms a right triangle such that
Therefore, the angle between the two radii is acos(r/R) and the area of the sector OAB is given by:
Furthermore:
which means the area of triangle ABO is 
The area of the pink area is the sector minus the triangle ABO, so you have:
(edited to clean up LaTeX)
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nice post
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