Question

The sum of diameters of two circles is 112cm and the sum of their areas is 5236cm². Find the radii of the two circles.

Answer 1

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

Given 2R + 2r
= 112cm R + r
= 56cm.
So, R = 56 - 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 + πR²
= π(r² + R²)
= 5236
⇒ r² + R² = 1666
⇒ r² + 56
⇒ 2r² - 112r + 1470 = 0
⇒ r² - 56r + 735 = 0
⇒ r² - 35r - 21r + 735 = 0
⇒ r(r - 35) - 21(r - 35) = 0
⇒ (r - 35)(r - 21) = 0
⇒ r = 35, 21
So, one of the two circles touching externally has a radius of 35cm and the other has radius 21cm.