1995 AIME Problems/Problem 14

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Problem

In a circle of radius 42, two chords of length 78 intersect at a point whose distance from the center is 18. The two chords divide the interior of the circle into four regions. Two of these regions are bordered by segments of unequal lenghts, and the area of either of them can be expressed uniquley in the form $\displaystyle m\pi-n\sqrt{d},$ where $\displaystyle m, n,$ and $\displaystyle d_{}$ are positive integers and $\displaystyle d_{}$ is not divisible by the square of any prime number. Find $\displaystyle m+n+d.$

Solution

See also