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Question

Two concentric circles are of radii $$8cm$$ and $$5cm$$.Find the length of the chords of the larger circle which touches the smaller circle.


Solution

As perpendicular from centre bisects the chord

$$\Rightarrow QR=PR$$

In $$\Delta ORQ$$ by Pythagoras theorem,

$$OQ^2=OR^2+RQ^2$$

$$\Rightarrow QR=\sqrt{64-25}=\sqrt{39}$$

Also,

$$PQ=2RQ$$

$$\Rightarrow PQ=2\sqrt{39}$$cm.

1214502_1396325_ans_6ebd7dab9b324ebabac43247130e494f.png

Mathematics

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