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  • Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

7.   Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

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In the above figure, Pq is the chord to the larger circle, which is also tangent to a smaller circle at the point of contact R.
We have,
radius of the larger circle OP = OQ = 5 cm
radius of the small circle (OR) = 3 cm

OR \perp PQ  [since PQ is tangent to a smaller circle]

According to question,

In \DeltaOPR and \DeltaOQR
\anglePRO = \angleQRO  {both 90^0}

OR = OR {common}
OP = OQ {both radii}

By RHS congruence \DeltaOPR \cong \DeltaOQR
So, by CPCT
PR = RQ
Now, In \Delta OPR,
by using pythagoras theorem,
PR = \sqrt{25-9} =\sqrt{16}
PR = 4 cm
Hence, PQ  = 2.PR =  8 cm 

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manish

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