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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`
Solution
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 `underlinebb("R"_1^2 + "R"_2^2 = "R"^2)`.
Explanation:
According to the question,
Area of circle = Area of first circle + Area of second circle
∴ `π"R"^2 = π"R"_1^2 + π"R"_2^2`
⇒ `"R"^2 = "R"_1^2 + "R"_2^2`
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