Question 14
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 lengths, and the area of either of them can be expressed uniquely in the form $m\pi-n\sqrt d,$ where $m,$ $n,$ and $d$ are positive integers and $d$ is not divisible by the square of any prime. Find $m+n+d.$