Question

Two circles touch each other externally. The sum of their areas is 58π cm² and the distance between their centers is 10 cm. Find the radii of the two circles.

Answer 1

Let r and R be the radius of the two circles.
r + R = 10                ....(1)
πr² + πR² = 58π      .....(2)

Putting the value of r in (2)
r² + R² = 58
( 10 - R )² + R² = 58
100 - 20R + R² + R² = 58
2R² - 20R + 42 = 0
R² - 10R + 21 = 0
( R - 3 )( R - 7 ) = 0
R = 3, 7.
Hence the radius of the two circles is 3cm and 7cm respectively.