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Question
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.
Solution
Let AB be a chord of a circle with centre O and radius 13cm 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 = `1/2`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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