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

8 cm

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6 cm

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4 cm

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10 cm

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Solution

The correct option is A 8 cm
$O M = 3 c m, O P = 5 c m$
$∠ M = 90^{o}$
Right angle $△ P O M$
Pythagoras throram
$O P^{2} = O M^{2} + P M^{2}$
$5^{2} = 3^{2} + P M^{2}$
$P M^{2} = 25 - 9 = 16$
$P M = 4 c m$
$∴ P Q = 2 P M = 2 \times 4 = 8 c m$

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