Question

The radius of a circle is 5 cm. The distance of a chord from the centre is 4 cm. Find the length of the chord.

Answer 1

In the given circle, radius OA = 5 cm: distance of the chord AB from the centre is 4 cm.
So, seg AM = seg MB (Perpendicular drawn from the centre to a chord bisects the chord)
By using Pythagoras theorem, in right triangle AOM,
AM² + OM² = OA²
⇒ AM² + 4² = 5²
⇒ AM² +16 = 25
⇒ AM² = 25 – 16
⇒ AM² = 9
⇒ AM = 3 cm
But seg AM = seg MB = 3 cm
∴ Seg AB = seg AM + seg MB = 3 cm + 3 cm = 6 cm
Therefore, the length of the chord is 6 cm.