The radius of a circle is 13 cm and the length of one of its chord is 10 cm.

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asked Mar 9 in Class X Maths by navnit40 (-2,979 points)

The radius of a circle is 13 cm  and the length of one of its chord is 10 cm. Find the distance of the  chord from the centre.

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answered Mar 9 by aditya23 (-878 points)

Let AB be a chord of a circle with centre O and radius 13 cm such that  AB = 10 cm.

From O, draw OL ⊥ AB. Join OA.

Since, the perpendicular from the centre of a circle to a chord bisects the chord.

∴  AL = LB = ½ AB = 5 cm

Now, in right triangle OLA, we have

OA2 = OL2 + AL2

⇒  132 = OL2 = 52

⇒  132 – 52 = OL2

⇒ OL2 = 144

⇒  OL = 12 cm.

Hence, the distance of the chord from the centre is  12 cm.

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