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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 D 5 cmGiven - 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. ∵ OL⊥PQand 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

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