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2017 preRMO p26 area between parallel chords

Source:

August 20, 2019
geometryChordsparallelareacircle

Problem Statement

Let ABAB and CDCD be two parallel chords in a circle with radius 55 such that the centre OO lies between these chords. Suppose AB=6,CD=8AB = 6, CD = 8. Suppose further that the area of the part of the circle lying between the chords ABAB and CDCD is (mπ+n)/k(m\pi + n) / k, where m,n,km, n, k are positive integers with gcd(m,n,k)=1(m, n, k) = 1. What is the value of m+n+km + n + k ?
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