A chord of a circle is 12 cm in length and its distance from the centre is 7 cm. Find the length of the chord of the same circle which is at a distance of 6 cm from the centre.

Using the perpendicular bisector property of a chord, the radius squared equals 7 squared plus 6 squared, yielding 85. For the second chord at a distance of 6 cm, half its length squared equals the radius squared minus 6 squared, which is 85 minus 36 to give 49. Taking the square root gives a half-length of 7 cm, so the full chord is 14 cm.

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