Question

The sum of the radii of two circles is $140$cm and difference of their circumference is $88$cm. Find the diameter of the circles.

Answer 1

Let the radii be $r_1$ & $r_2$

Then $r_1+r_2=140$cm ……….$\left(1\right)$

$c_1-c_2=88$cm

$\Rightarrow 2\pi r_1-2\pi r_2=88$cm

$\Rightarrow 2\pi (r_1-r_2)=88$

$r_1-r_2=44/\pi =14$cm …………$\left(2\right)$

Adding equation $\left(1\right)$ & $\left(2\right)$

$\Rightarrow 2r_1=154$cm

$r_1=77$cm

Subtracting equation $\left(1\right)$ & $\left(2\right)$

$2r_2=126$

$r_2=63$cm.