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 ______.

Options

• R₁ + R₂ = R

• `"R"_1^2 + "R"_2^2 < "R"^2`

• R₁ + R₂ < R

• `"R"_1^2 + "R"_2^2 < "R"^2`

Answer 1

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 `"R"_1^2 + "R"_2^2 < "R"^2`.

Explanation:

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

∴ πR² = πR₁² + πR₂²

⇒ R² = R₁² + R₂²