JAMB 2011 · UTME · Q29✱✱

A chord of a circle of radius $7\text{ cm}$ is $5\text{ cm}$ from the centre of the circle. What is the length of the chord?

Worked solution (try it first)

The perpendicular from the centre to a chord bisects it.
The radius, the 5 cm distance and half the chord make a right-angled triangle with hypotenuse 7.
Pythagoras: half the chord is $\sqrt{7^2 - 5^2} = \sqrt{24} = 2\sqrt6$ cm.
So the chord is $2 \times 2\sqrt6 = 4\sqrt6$ cm, option A.