Question

In figure there are two concentric circles with centre O and of radii 5 cm and 3 cm. From an external point P tangents PA and PB are drawn to these circles. If AP = 12 cm find the length of BP

• A. $4\sqrt{10}$ cm
• B. $2\sqrt{10}$ cm
• C. $\sqrt{10}$ cm
• D. $3\sqrt{10}$ cm

Answer 1

The correct option is A $4\sqrt{10}$ cm

Two concentric circles with center O. OA is 5 cm and OB is 3 cm.
Join OP.
Now, in $△OAP$
$\angle OAP={90}^{\circ }$ (Angles between radius and tangent)
$O{A}^2+A{P}^2=O{P}^2$
$5^2+{12}^2=O{P}^2$
$OP=13$ cm
In $△OBP$,
$O{B}^2+B{P}^2=O{P}^2$
$3^2+B{P}^2={13}^2$
$BP=\sqrt{160}=4\sqrt{10}$ cm