Question

Sum of the areas of two circles of radii r1 and r2 is equal to the area of circle of radius r if

Answer 1

π r1² + πr2² = πr²

π is common and cancel from each side

then we get ....

             r1² +r2² = r²

    hope it helps you

Answer 2

Answer: If  $r=\sqrt{r_{1} ^{2}+ r_{2} ^{2}}$

Step-by-step explanation:

radius of first circle = $r_{1}$

radius of second circle =$r_{2}$

As we know area of circle is $\pi R^{2}$ where R is the radius of the circle.

According to question

area of circle of radius  $r_{1}$ + area of circle of radius  $r_{2}$ = area of circle of radius r

$\pi r_{1} ^{2}+ \pi r_{2} ^{2}=\pi r ^{2}\\\\\Rightarrow r_{1} ^{2}+ r_{2} ^{2}= r ^{2}\\\\\Rightarrow r=\sqrt{r_{1} ^{2}+ r_{2} ^{2}}$

Therefore ,sum of the areas of two circles of radii  $r_{1}$ and $r_{2}$ is equal to the area of circle of radius r if  $r=\sqrt{r_{1} ^{2}+ r_{2} ^{2}}$