The radius of a circle is 13 cm and the length of one of its chords is 24 cm. Find the distance of the chord from the centre.

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asked Sep 26, 2018 in Class IX Maths by navnit40 (-3,089 points)

The radius of a circle is 13 cm and the length of one of its chords is 24 cm. Find the distance of the chord from the centre.

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answered Sep 26, 2018 by priya12 (-11,407 points)

Solution  :-

Let PQ be a chord of a circle with centre O and radius 13cm such that PQ = 24cm.
From O, draw OM perpendicular PQ and join OP.
As, the perpendicular from the centre of a circle to a chord bisects the chord.
∴  PM = 12cm
In △OMP, we have
 OP2 = OM2 + PM2
⇒ 132 = OM2 + 122
⇒ OM = 5cm.                                                                                                                                                      Hence, the distance of the chord from the centre is 5cm.

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