A chord of length 24 cm is at a distance of 5 cm from the centre of a circle. What is its area?

Let the radius of the circle = r

Length of the chord = 24 cm

The perpendicular from the centre to the chord bisects the chord

$$=$$>  BA = AC = 12 cm

From the figure

In $$\triangle\ $$OAB,

$$OA^2+AB^2=OB^2$$

$$=$$>  $$5^2+12^2=r^2$$

$$=$$>  $$25+144=r^2$$

$$=$$>  $$r^2=169$$

$$=$$>  $$r=13$$ cm

Radius of the circle = 13 cm

$$\therefore\ $$Area of the circle = $$\pi\ r^2=\frac{22}{7}\times\left(13\right)^2=\frac{22}{7}\times169=531.14cm^2$$

Hence, the correct answer is Option C