Question

Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 6 cm respectively, as shown in the figure. If AP = 6 cm then find the length of BP.

• A. 8 cm
• B. 16 cm
• C. 10 cm
• D. 6 cm

Answer 1

The correct option is A

8 cm

We have

OA $\perp$ AP and OB $\perp$ BP [ The tangent at any point of a circle is perpendicular to the radius through the point of contact].

Join OP.

In right $\Delta$ OAP, we have

OA = 8 cm, AP = 6 cm

$\therefore O{P}^2=O{A}^2+A{P}^2$ [by Pythagoras theorem]

$\Rightarrow OP=\sqrt{O{A}^2+A{P}^2}=\sqrt{8^2+6^2}cm=\sqrt{100}cm=10cm$

In right $\Delta$ OBP, we have

OB = 6 cm, OP = 10 cm

$\therefore O{P}^2=O{B}^2+B{P}^2$
[by Pythagoras' theorem]

$\Rightarrow BP=\sqrt{O{P}^2-O{B}^2}=\sqrt{{10}^2-6^2}cm=\sqrt{64}cm$

Thus, the length of BP
$=\sqrt{64}cm$ = 8 cm.