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Question

Two concentric circles are of radii 7 cm and r cm respectively, where r > 7. A chord of the larger
Circle, of length 48 cm, touches the smaller circle. Find the value of r.

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Solution

Let O be the centre of the two concentric circles. Let PQ be the chord of larger circle touching the smaller circle at M. This can be represented diagrammatically as:

We have PQ = 48 cm.
Radius of the smaller circle, OM = 7 cm
Let the radius of the larger circle be r, i.e. OP = r
Since PQ is a tangent to the inner circle, OM ΛPQ
Thus, OM bisects PQ.
PM=MQ=482cm=24cm
Now applying Pythagoras Theorem in ΔOPM
OP2=OM2+PM2
OP2=(7cm)2+(24cm)2=(49+576)cm2=625cm2=(25cm)2
OP=25cm
Radius of the larger circle is 25 cm.
Thus, the value of r is 25 cm.


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