Question

Two circles touch each other externally. The sum of their areas is 58πcm² and the distance between their centres us 10cm. Find the radii of the two circles.

Answer 1

Let one of the two circles touching externally have a radius of R and the other have radius r

Given R + r = 10cm.
So, R = 10 - r
The Area of a Circle with radius r = πr²
The Area of a Circle with radius R = πR²
Sum of the areas of the two circles
= πr² + πR
= π(r² + R²)
= 58π
⇒ r² + R² = 58
⇒ r² + (10 - r)² = 58
⇒ r² + 100 + r² - 20r = 58
⇒ 2r² - 20r + 42 = 0
⇒ r² - 10r + 21 = 0
⇒ r² - 7r - 3r + 21 = 0
⇒ r(r - 7) -3(r - 7) = 0
⇒ (r - 7)(r - 3) = 0
⇒ r = 7, 3
So, one of the two circles touching externally has a radius of 7cm and the other have radius 3cm.