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

The area of a circle is given by the formula A = πr², where r is the radius of the circle.

If the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle with radius R, we can express this as follows:

πR1² + πR2² = πR²

This equation tells us that the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle with radius R.

To simplify, we can divide through by π:

R1² + R2² = R²

This is the relationship between the radii R1, R2, and R. It tells us that the square of the radius of the larger circle (R) is equal to the sum of the squares of the radii of the two smaller circles (R1 and R2). This is similar to the Pythagorean theorem in a right triangle, where the square of the hypotenuse is equal to the sum of the squares of the other two sides.