If the sum of the areas of two circles with radii R1 and R2 is equal to the area ofa circle of radius R, then(A) R1 + R 2 = R (B) 21R + 22R = R 2(C) R1 + R 2 < R (D) 2 2 21 2R R R
Question
If the sum of the areas of two circles with radii R1 and R2 is equal to the area ofa circle of radius R, then(A) R1 + R 2 = R (B) 21R + 22R = R 2(C) R1 + R 2 < R (D) 2 2 21 2R R R
Solution
The area of a circle is given by the formula πr², where r is the radius of the circle.
Given that the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle of radius R, we can write the equation as:
πR1² + πR2² = πR²
Dividing through by π, we get:
R1² + R2² = R²
This is the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Therefore, the correct answer is (B) R1² + R2² = R².
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