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

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Solution

In the given circle, radius OA = 13 cm; length of the chord AB is 10 cm.
So, seg AM = seg MB (Perpendicular drawn from the centre to a chord bisects the chord)
Seg AM = 5 cm
By using Pythagoras theorem, in right triangle AOM,
AM² + OM² = OA²
⇒ 5² + OM² = 13²
⇒ 25 + OM² = 169
⇒ OM² = 169 – 25
⇒ OM² = 144
⇒ OM = 12 cm
Therefore, the distance of the chord AB from the centre is 12 cm.

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