MathDB

Alice is standing on the circumference of a large circular room of radius

10

. There is a circular pillar in the center of the room of radius

5

that blocks Alice’s view. The total area in the room Alice can see can be expressed in the form

\frac{m\pi}{n} +p\sqrt{q}

, where

m

and

n

are relatively prime positive integers and

p

and

q

are integers such that

q

is square-free. Compute

m + n + p + q

. (Note that the pillar is not included in the total area of the room.) https://cdn.artofproblemsolving.com/attachments/5/1/26e8aa6d12d9dd85bd5b284b6176870c7d11b1.png

Problem Statement