# The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the area of the two circles.

Let r be the radius of the circle whose area is equal to the sum of the area of the circles of radii 8 cm and 6 cm.

$$\because \pi r^2 \ = \ \pi (8)^2 \ + \ \pi(6)^2$$

$$\Rightarrow r^2 \ = \ 8^2 \ + \ 6^2$$

$$\Rightarrow \ r^2 \ = \ 64 \ + \ 36 \$$
$$\Rightarrow \ r \ = \ 10$$

Hence, the radius of the new circle is 10 cm.