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Let A B and C D 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 A B and C D is (m +n) / k , where m, n, k are positive integers with gcd ( m , n , k )=1 . What is the value of m + n + k ?

Correct answer

75

Step-by-step solution

aligned & A=2 [ 1 2 25 ]+ 1 2 3 8+ 1 2 4 6 & = [ - ( ₁+ ₂ ) ]= [ - ( ⁻¹ 4 3 + ⁻¹ 3 4 ) ] & = 2 & A=24+ 25 2 A= 48+25 2 & (m+n+k)=(48+2+25)=75 aligned

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