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Question

Two concentric circles are of radii 5cm and 3cm.

Find the length of the chord of the larger circle which touches the smaller circle.


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Solution

Solve for length of chord:

In OAP and OFP

OA=OF (radius of same circle)

OP=OP (given)

APO=FPO=90° (angle made by tangent and radius is 90°)

Therefore, OAPOFP (by RHS congruency criterion)

So, AP=FP (by C.P.C.T.)

Now, in OAP

OA=5cm (radius of larger circle)

OP=3cm (radius of smaller circle)

OA2=(OP)2+(AP)2 (By Pythagoras theorem)

52=(3)2+(AP)225-9=(AP)2(AP)2=16AP=4

Length of chord =2×AP=8cm

Hence, the length of the chord of the larger circle which touches the smaller circle is 8cm.


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