Find the length of a chord which is at a distance of 12 cm from the centre of a circle of radius 13 cm.

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asked Sep 26, 2018 in Class IX Maths by navnit40 (-4,746 points)

Find the length of a chord which is at a distance of 12 cm from the centre of a circle of radius 13 cm.

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answered Sep 26, 2018 by priya12 (-12,564 points)

Solution  :-

Let AB be a chord of circle with centre O and radius 13cm. Draw OM perpendicular AB and join OA.
In the right triangle OMA, we have
  OA2 = OM2 + AM2
⇒  132 = 122 + AM2
⇒  AM2  = 169 - 144 = 25                                                                                                                                   ⇒  AM = 5cm.

As the perpendicular from the centre of a chord bisects the chord.Therefore,
 AB = 2AM = 2 x 5 = 10cm.

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