Find the length of a chord which is at a distance of 5 cm from the centre of a circle of radius 13 cm.

20 cm

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22 cm

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24 cm

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26 cm

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Solution

The correct option is D. 24 cm

$O A = 5 c m$

Radius $O B = 13 c m$

Therefore, $A B = \sqrt{({O B}^{2}) - ({O A}^{2})}$
$\Rightarrow A B = \sqrt{13^{2} - 5^{2}}$
$\Rightarrow A B = \sqrt{169 - 25}$
$\Rightarrow A B = \sqrt{144}$

$A B = 12 c m$

The required chord is $B C = 2 A B$ .

Thus, $B C = 24 c m$

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Find the length of a chord which is at a distance of 5 cm from the centre of a circle of radius 13 cm.

The correct option is D. 24 cm OA=5cm Radius OB=13cm Therefore, AB=√(OB2)−(OA2)⇒AB=√132−52⇒AB=√169−25⇒AB=√144 AB=12cm The required chord is BC=2AB. Thus, BC=24cm