Question

Two unequal spherical balls lie on a field touching each other. The radius of the smaller ball is $9cm$ and the point of contact is $12cm$ above the field. Find the sum of the radii of the two balls.

Answer 1

Let radius of other circle be $O^{1}P=r$

$OP=9cm$ & point of contact of two circles be P such that $PR=12cm$

$\therefore$ $△PQO\sim △O^{1}SO$ [By AA similarity]

$\therefore$ $\frac{PQ}{OP}=\frac{O^{1}S}{{OO}^1}$ $[O^{1}S=O^{1}T-ST=r-9\&{OO}^1=OP+{PO}^1]$

$\Rightarrow \frac{12-9}{9}=\frac{r-9}{r+9}\Rightarrow \frac{1}{3}=\frac{r-9}{r+9}\Rightarrow r+9=3r-27$

$\Rightarrow 2r=36\Rightarrow r=18$

Sum of radii $=9+18=27cm$