Question

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 circle
respectively. If PA = 10 cm, find the
length of PB up to one place of decimal.​

Answer 1

Answer:

answer for the question is given below

and the picture is given above

Explanation:

In the given figure,

PA and PB are the tangents drawn from P, to the outer circle and inner circle respectively.

PA=10cm

OA and OB are the radii and

PA and PB are two tangents to the circles respectively

So,

OA⊥PA and OB⊥PB

In right ΔOAP

By Pythagoras Theorem:

OP

2

=OA

2

+PA

2

=(6)

2

+(10)

2

OP

2

=136 ___(1)

From right ΔOBP,

OP

2

=OB

2

+PB

2

136=(4)

2

+PB

2

136=16+PB

2

[Using equation (1)]

we have PB

2

=136−16=120

Or PB=

120

cm=2

30

cm=2×5.47=10.9

Length of PB is 10.9cm

thank you I hope it will help you