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Question

In the given figure, two concentric circles are drawn. If the radius of an inner circle = 3 cm and the length of the chord of an outer circle which touches an inner circle = 8 cm then, find the radius of an outer circle.


A
7 cm
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B
10 cm
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C
6 cm
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D
5 cm
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Solution

The correct option is C 5 cm

Given - Radius of inner circle = 3 cm and PQ = 8 cm. PQ is the chord of the outer circle which touches the inner circle at L. Join OL and OP.
 

 OLPQand OL bisects chord PQ.

LP=12PQ

LP=12×8=4cm
so,
LP = 4 cm and OL = 3 cm (Radius of inner circle)

In right Δ OLP,

OP2=OL2+LP2

(OP)2=(3)2+42

OP2=9+16

OP2=25

OP=25=5 cm


Mathematics

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