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 find the relationship between $R_1$, $R_2$ and $R_3$.

Given: Sum of the areas of two circles with radii $R_1$ and $R_2$ is equal to the area of a circle of radius $R$.

To do: To find the relationship between $R_1$, $R_2$ and $R_3$.

Solution:

Area of the circle with radius $( R_1)=\pi R_1^2$

Area of the circle with radius $( R_2)=\pi R_2^2$

Area of the circle with $( R)=\pi R^2$

According to the question,

Area of the circle with radius$( R)=$Area of the circle$( R_1)+$Area of the circle $( R_2)$

$\Rightarrow \pi R^2=\pi R_1^2+\pi R_2^2$

$\Rightarrow R^2=R_1^2+R_2^2$

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Updated on: 10-Oct-2022

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