Question

Diameter of a circle is 26 cm and length of a chord of the circle is 24 cm. Find the distance of the chord from the centre.

Answer 1

Diameter = 26 cm
chord = 24 cm
Perpendicular drawn from the centre of the circle to the chord bisects the chord.
OD ⊥ AB
So, AD = DB
AO = OC (Radii)
In ∆ODA,
$$\begin{gathered} {\mathrm{OD}}^2+{\mathrm{AD}}^2={\mathrm{OA}}^2 \\ \Rightarrow {\mathrm{OD}}^2+{12}^2={13}^2 \\ \Rightarrow {\mathrm{OD}}^2+144=169 \\ \Rightarrow {\mathrm{OD}}^2=169-144=25 \\ \Rightarrow \mathrm{OD}=5\mathrm{cm} \end{gathered}$$
Thus, the distance of the chord from the centre is 5 cm.