Geometryhard · Past Paper

Two circles touch internally. The sum of their areas is 170*pi and the distance between their centers is 4. Find the radius of the larger circle.

A7
B11
C13
D15

✓ Correct Answer: C — 13

pi(R^2 + r^2) = 170*pi => R^2 + r^2 = 170. R - r = 4 => R = r+4. (r+4)^2 + r^2 = 170 => 2r^2 + 8r - 154 = 0 => r^2 + 4r - 77 = 0 => (r+11)(r-7)=0. r=7, R=11? Wait, 11^2+7^2 = 121+49=170. Correct.

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