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  • The radius of a circle is 13 cm and the length of one of its chords is 24 cm. Then the distance of the chord from the centre is Option: 1 1

The radius of a circle is 13 cm and the length of one of its chords is 24 cm. Then the distance of the chord from the centre is 

Option: 1

10 cm


Option: 2

5 cm


Option: 3

6 cm


Option: 4

None of these


Answers (1)

best_answer

Let AB be a chord of the given circle with centre O and radius 13 cm.

Then, OA = 13 cm and AB = 24 cm

As we know that the perpendicular from the centre of a circle to a chord bisects the chord..

AL = (1/2)AB = 12 cm

Consider the right angle triangle OLA, using pythagores theorem

\begin{aligned} O A^{2}&=O L^{2}+A L^{2} \\ \Rightarrow O L^{2}&=O A^{2}-A L^{2} =13^2-12^2\\ \Rightarrow O L&=\sqrt{25} \mathrm{cm}=5\mathrm{cm} \end{aligned}

The distance of the chord from the centre is 5 cm

Posted by

Ajit Kumar Dubey

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