Question

There are two cocentric circles with centre $O$ of radii $5cm$ and $2cm$. From an external point $P$, tangents $PA$ & $PB$ are drawn to these circles. If $PA=10cm$, find the length of $BP$.

Answer 1

$r_1=5cm$

$r_2=2cm$

$AP=10cm$

To find : $BP=?$

$\therefore$ In $△atOAP(since\angle OAP={90}^o)$ [tangent subtend right angle]

$O{A}^2+A{P}^2=OP$

$r_1^2+{10}^2=O{P}^2$

$O{P}^2=5^2+{100}^2$

$=25+100=125=O{P}^2---\left(1\right)$

$\therefore$ In $rt△OBP$

$O{B}^2+B{P}^2=O{P}^2$

$\Rightarrow r_2^2+B{P}^2=125$

$\Rightarrow B{P}^2=125-2^2$

$B{P}^2=125-4$

$BP=\sqrt{121}$

$BP=11cm$