Question

The length of a chord of a circle of 16.8 cm, radius is 9.1 cm. Find its distance from the centre.

Answer 1

Length of the chord = 16.8 cm
Radius = 9.1 cm
Let the distance from the centre of the chord be d.
Perpendicular drawn from the centre of the circle to the chord bisects the chord.
So, AC = CB = $\frac{16.8}{2}=8.4$ cm
In $△$AOC,
Applying the Pythagoras theorem we have
$$\begin{gathered} {\mathrm{OC}}^2+{\mathrm{AC}}^2={\mathrm{AO}}^2 \\ \Rightarrow d^2+8.4^2=9.1^2 \\ \Rightarrow d^2=82.81-70.56 \\ \Rightarrow d^2=12.25 \\ \Rightarrow d=3.5\mathrm{cm} \end{gathered}$$
Thus, the distance of chord from the centre is 3.5 cm.