Question

The radii of the two circles are $19\text{cm}$ and $9\text{cm}$ respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

Answer 1

Let $r_1$ and $C_1$ be the radius and circumference, respectively of 1st circle and $r_2$ and $C_2$ be the radius and circumference, respectively of 2nd circle.

Let $r_3$ and $C_3$ be the radius and circumference, respectively of the required circle.

$r_1=19\text{cm}$ ...Given

$⟹C_1=2\pi r_1$

$\therefore C_1=2\pi \times 19=38\pi \text{cm}$ ...(1)

$r_2=9\text{cm}$ ...Given

$⟹C_2=2\pi r_2$

$\therefore C_2=2\pi \times 9=18\pi \text{cm}$ ...(2)

$C_3=C_1+C_2$ ....Given

$\therefore C_3=38\pi +18\pi$ ....From (1) and (2)

$C_3=56\pi \text{cm}$

$⟹2\pi r_3=56\pi$

$\therefore r_3=28\text{cm}$

The radius of the required circle is $28\text{cm}$