Question

If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then

(A) R₁ + R₂ = R (B) R₁² + R₂² = R²

(C) R₁ + R₂ < R (D) R₁² + R₂² < R²

Answer 1

(B) R₁² + R₂² = R²

Explanation:

According to the question,

Area of circle = Area of first circle + Area of second circle

∴ πR² = πR₁² + πR₂²

⇒ R² = R₁² + R₂²

∴ Option B is correct.