Question

Two circles touch each other externally. The sum of their areas is $74\pi c{m}^2$ and the distance between their centre is $12cm$. Find the diameter of the circle.

Answer 1

R.E.F image

$Let{A}_1$ be the area of circle $c_1$

$Let{A}_1$ be the area of circle $c_1$

$Let{r}_1$ be the radius of circle $c_1$

$Let{r}_2$ be the radius of circle $c_2$

$r_1{+}_2=12cm.----\left(1\right)$

$A_1+A_2=74\pi c{m}^2$

$\pi r_1^2+\pi r_2^2=74\pi$

$r_1^2+r_2^2=74-----2$

Form$\left(1\right),r_1=12-r_2----\left(3\right)$

Put (3) in (2)

$(12-r_2{)}^2+r_2=74$

$144-24r_2+r_2^2=74$

$144-24r_2+2r_2^2=74$

$2r_2^2-24r^2+144-74=0$

$2r_2^2-24r_2+70=0$

$r_2^2-12r_2+35=0$

$r_2^2-5r_2-7r_2+35=0$

$r_2(r_2-5)-7(r_2-5)=0$

$(r_2-7)(r_2-5)=0$

$1f=r_2-7=0r_2=-5=0$

$1f{r}_2=71f{r}_2=5$

$n=12-7r_1=12-5$

$n=5cm{r}_1=7cm.$

$d_1=2r_1,d_2=2r_2{d}_1{r}_1,d_2=2r_2$

$d_1=10cm{d}_1=14cm$

$d_2=14cm{d}_2=10cm$