Question

In the figure, the radii of two concentric circles with centre $O$ are $5cm$ and $3cm$ $PA$ and $PB$ are tangents to these circles. If $PA=12cm$. Find $BP$

Answer 1

$OD=5cm$ $OB=3cm$ $PA=12cm$

$\angle OAP=\angle OBP=90°$

So, $△OAP$

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

$OP=\sqrt{{12}^2+5^2}=\sqrt{169}=13cm$

$△OBB$

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

$BP=\sqrt{{13}^2-3^2}=\sqrt{160}=4\sqrt{1}0cm$