Multiple choice

If the sum of the areas of two circles with radii $R_1$ and $R_2$ is equal to the area of a circle of radius R, then

  1. $R_{1}+R_{2}=R$
  2. $R_{1}^{2}+R_{2}^{2}=R^{2}$
  3. $R_{1}+R_{2} < R$
  4. $R_{1}^{2}+R_{2}^{2} < R^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area of circle 1 = pi * R1^2. Area of circle 2 = pi * R2^2. Area of circle 3 = pi * R^2. Sum of areas: pi * R1^2 + pi * R2^2 = pi * R^2. Dividing by pi gives R1^2 + R2^2 = R^2.

AI explanation

The area of a circle is calculated as pi times the radius squared, so the sum of the areas of the two circles is pi times R sub one squared plus pi times R sub two squared. This total area equals pi times R squared. Dividing the entire equation by pi leaves R sub one squared plus R sub two squared equals R squared.

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