You visited us 1 times! Enjoying our articles? Unlock Full Access!

Pair of Tangents from a Point

In the given ...

Question

In the given figure, $O$ is the centre of each one of two concentric circles of radii $4 c m$ and $6 c m$ respectively. $P A$ and $P B$ are tangents to outer and inner circle respectively. If $P A = 10 c m$ , then the length of $P B$ , up to two places of decimal is

13.60cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

11.60cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

10.95cm

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

15.23cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D 10.95cm
$G i v e n - O i s t h e c e n t r e o f t w o c o n c e n t r i c c i r c l e s . T h e r a d i u s o f t h e o u t e r c i r c l e i s 6 c m a n d t h e r a d i u s o f t h e i n n e r c i r c l e i s 4 c m . P A = 10 c m i s a t a n g e n t f r o m a p o i n t P t o t h e o u t e r c i r c l e a n d P B i s a t a n g e n t f r o m t h e s a m e p o i n t P t o t h e i n n e r c i r c l e . T o f i n d o u t - P B = ? S o l u t i o n - w e j o i n O A, O B & O P . ∴ O A & O B a r e r a d i i t h r o u g h t h e p o i n t s o f c o n t a c t A & B o f t h e t a n g e n t s P A & P B r e s p e c t i v e l y . ∴ O A ⊥ P A & O B ⊥ P B . i . e Δ O A P & Δ O B P a r e r i g h t t r i a n g l e s w i t h O P a s c o m m o n h y p o t e n u s e . S o, a p p l y i n g P y t h a g o r a s t h e o r e m, w e g e t O P = \sqrt{{O A}^{2} + {A P}^{2}} = \sqrt{10^{2} + 6^{2}} c m = \sqrt{136} c m . A n d P B = \sqrt{{O P}^{2} - O B^{2}} = \sqrt{136 - 4^{2}} c m = \sqrt{120} c m = 10.95 c m . A n s - O p t i o n C .$

Suggest Corrections

Similar questions

Q. In the given figure, O is the centre of two concentric circles of radii 4 cm and 6 cm respectively. PA and PB are tangents to the outer and inner circles, respectively. If PA = 10 cm, find the length of PB up to one decimal place.

Q. In the given figure, O is the centre of two concentric circles of radii 5 cm and 3 cm. From an external point P tangents PA and PB are drawn to these circles. If PA = 12 cm then PB is equal to

(a)

5 \sqrt{2} cm

(b)

3 \sqrt{5} cm

(c)

4 \sqrt{10} cm

(d)

5 \sqrt{10} cm

Q. If figure, the radii of two concentric circles with centre

O

are

5 c m

and

3 c m

P A

and

P B

are tangents to these circles. If

P A = 12 c m

. find

B P

Q. Tangents

P A

and

P B

are drawn from an external point

P

to two concentric circle with centre

O

and radii

8 c m

and

5 c m

respectively, as shown in figure. If

A P = 15 c m,

then find the length of

B P .

In the given figure, PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA $⊥$ PB, then the length of each tangent is

(a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm

Join BYJU'S Learning Program

In the given figure, O is the centre of each one of two concentric circles of radii 4cm and 6cm respectively. PA and PB are tangents to outer and inner circle respectively. If PA=10cm, then the length of PB, up to two places of decimal is

In the given figure, $O$ is the centre of each one of two concentric circles of radii $4 c m$ and $6 c m$ respectively. $P A$ and $P B$ are tangents to outer and inner circle respectively. If $P A = 10 c m$ , then the length of $P B$ , up to two places of decimal is