Question

Two circles touch externally. The sum of their areas is 130 π sq cm and distance between their centres is 14 cm. What is the radius of the bigger circle?
1. 8
2. 10
3. 11
4. 13

Answer 1

Correct Answer - Option 3 : 11

Given:

The sum of their areas = 130 π sq cm

Distance between their centers = 14 cm.

Formula Used:

Area of circle = πr²

Calculation:

Let assume that radius of circle 1 = x

So, radius of circle 2 = 14 - x

Area of circle 1 = π(x)²

Area of circle 2 = π(14 - x)²

According to question

⇒ π(x)2 + π(14 - x)2 = 130π

⇒ x² + 196 - 28x + x² = 130

⇒ 2x² - 28x + 66 = 0

⇒ x² - 14x + 33 = 0

⇒ (x - 11)(x - 3) = 0

⇒ x = 11

⇒ x = 3

∴ The radius of bigger circle is 11 cm

The correct option is 3 i.e. 11 cm