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  • A chord is at a distance of 8 cm from the centre of a circle of radius 17 cm. Then the  length of the chord isOption: 1 10 cm<div

A chord is at a distance of 8 cm from the centre of a circle of radius 17 cm. Then the  length of the chord is

Option: 1

10 cm


Option: 2

30 cm


Option: 3

15 cm


Option: 4

20 cm


Answers (1)

best_answer

Let AB be a chord of the given circle with centre O and radius 17 cm.

Then, OA = 17 cm and AB = 8 cm

 

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

Consider the right angle triangle OLA, using pythagores theorem

\begin{aligned} O A^{2}&=O L^{2}+A L^{2} \\ \Rightarrow A L^{2}&=O A^{2}-O L^{2} =17^2-8^2=289-64=225\\ \Rightarrow A L&=\sqrt{225} \mathrm{cm}=15\mathrm{cm} \end{aligned}

AB =  2 x AL = 20 cm

Posted by

Ritika Kankaria

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