Question

In two concentric circles, a chord of length 24 cm of larger circle becomes a
tangent to the smaller circle whose radius is 5 cm. find the radius of the larger
circle.

Answer 1

Answer:

Let O be the centre of concentric circles and APB be the chord of length 24 cm, of the larger circle touching the smaller circle at P.

Then, OP⊥AB and P is the mid-point of AB.

∴AP=PB=12 cm

In △OPA, we have

OA

2

=OP

2

+AP

2

[by pythagorus theorem]

⇒OA

2

=5

2

+12

2

=169

⇒OA=13 cm

Hence, the radius of the smaller circle is 13 cm.

solution

Answer 2

Let O be the center of concentric circles and APB be the chord of length 24 cm, of the larger circle touching the smaller circle at P.

Then, OP⊥AB and P is the mid-point of AB.

∴AP=PB=12 cm

In △OPA, we have

OA^2=OP^2+AP^2

[by Pythagorus theorem]

⇒OA^2=5^2+12^2

⇒OA^2 = 25+ 144

⇒OA^2 = 169

⇒OA = root of 169

⇒OA=13 cm

Hence, the radius of the smaller circle is 13 cm.

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