Question

Find the distance of a chord of length 12 cm from the centre
of the same circle if the radius is 15cm.​

Answer 1

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Let AB be a chord of a circle with centre O and radius 15 cm such that AB = 12 cm .

From O, draw OL perpendicular to AB . Join OA.

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

$\therefore \sf{\:AL = LB = \frac{1}{2} AB = 6 \: cm}$

In right triangle OLA, we have

$\bold{OA {}^{2} = OL {}^{2} + AL {}^{2} }$

$\implies \: {15}^{2} =OL {}^{2} + {6}^{2}$

$\implies \: OL {}^{2} = {15}^{2} - {6}^{2}$

$\implies \: OL {}^{2} = 225 - 36$

$\implies \: OL = \sqrt{189}$

$\implies \:OL =13.74 \: (approx)$

Hence, the distance of the chord from the centre is 13.74 cm.