Question

Let AB and CD be two parallel chords in a circle with radius 5 such that the centre O lies between these chords. Suppose AB = 6, CD = 8. Suppose further that the area of the part of the circle lying between the chords AB and CD is (mπ + n)/k, where m, n, k are positive integers with GCD(m, n, k) = 1. What is the value of m + n + k?

Answer 1

Area of the part of the circle lying between AB and CD is = 2[(ar ΔAOM) + area of sector AOC + (ar ΔCON)]

= (m + nπ)/k

⇒ m = 48, n = 25, k = 2

⇒ m + n + k = 75