Exercise 5.5

Find the length of the chord of a circle where the radius is 7 cm and perpendicular distance is 6 cm.

Explain why the following statement is true: If the perpendicular distance of a chord from the centre is \(d\) and the radius is \(r\), then the chord length is \(2\sqrt{r^2 − d^2}\).

In a circle, if the distance of chord AB from the centre is twice the distance of another chord CD from the centre, then can we conclude that CD = 2 AB? Give reasons for your answer.