Geometry Math

Lines y= 2x/3+3&y=5 cut the ring formed by circles (x-3)2+(y-5)2=64 and (x-3)2+(y-5)2=25 into four parts. Find the area of each of the four parts.

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  1. circle center is (3,5)
    lines intersect at (3,5) yay!

    ring has area pi(64-25) = 39pi = 122.91

    lines intersect at angle θ such that
    tanθ = 2/3
    θ = 33.69°

    the 4 parts are divided into two pairs, each pair occupying half the circle.

    33.69/180 = 0.187
    so, the semicircles are divided into areas of 22.98 and 99.93

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