## Book: RS Aggarwal - Mathematics

### Chapter: 12. Circles

#### Subject: Maths - Class 10th

##### Q. No. 11 of Exercise 12A

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11
##### In the given figure, O is the center 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.

In given Figure,

OA AP

[Tangent at any point on the circle is perpendicular to the radius through point of contact]

In right - angled OAP,

By Pythagoras Theorem

[i.e. (hypotenuse)2 = (perpendicular)2 + (base)2]

(OP)2 = (OA)2 + (PA)2

Given, PA = 10 cm and OA = radius of outer circle = 6 cm

(OP)2 = (6)2 + (100)2

(OP)2 = 36 + 100 = 136 [1]

Also,

OB BP

[Tangent at any point on the circle is perpendicular to the radius through point of contact]

In right - angled OBP,

By Pythagoras Theorem

[i.e. (hypotenuse)2 = (perpendicular)2 + (base)2]

(OP)2 = (OB)2 + (PB)2

Now, OB = radius of inner circle = 4 cm

And from [2]

(OP)2 = 136

136 = (4)2 + (PB)2

(PB)2 = 136 - 16 = 120

PB = 10.9 cm

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