If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, calculate the diameter of the larger circle (in cm). (CBSE 2012)

Suppose that C is the largest circle, C₁ is the circle with diameter 10 cm and C₂ is the circle with diameter 24 cm aNd R, R₁ and R₂ are the radius of these circles respectively.

The diagram is given below:

Given: R₁ = 5 cm [∵, Diameter = 10 cm]

R₂ = 12 cm [∵, Diameter = 24 cm]

Area of circle C = Area of circle C₁ + Area of circle C₂

⇒ πR² = πR₁² + πR₂²

⇒ πR² = π (R₁² + R₂²)

⇒ R² = (5)² + (12)²

⇒ R² = 25 + 144 = 169

⇒ R = √169 = 13

If the radius of the largest circle is 13, then diameter is 2R.

Diameter = 2R

⇒ Diameter = 2(13) = 26

Hence, diameter of the largest circle is 26 cm.