Question

The radius of a circle is 6 cm. The perpendicular distance from the centre of the circle to the chord which is 8 cm in length, is

(a) $\sqrt{5}\mathrm{cm}$

(b) $2\sqrt{5}\mathrm{cm}$

(c) $2\sqrt{7}\mathrm{cm}$

(d) $\sqrt{7}\mathrm{cm}$

Answer 1

(b) $2\sqrt{5}\mathrm{cm}$

We will represent the given data in the figure

We know that perpendicular drawn from the centre to the chord divides the chord into two equal parts.

So , AM = MB = $\frac{AB}{2}=\frac{8}{2}$ = 4 cm.

Using Pythagoras theorem in the ΔAMO,

Hence, the correct answer is option (b).