Question

Radius of a circle with centre O is 41 units. Length of a chord PQ is 80 units, find the distance of the chord from the centre of the circle.

Answer 1

We know that perpendicular drawn from the centre of the circle to the chord bisects the chord.
PR = RQ = 40 unit
In $△$OPR,
$$\begin{gathered} {\mathrm{OR}}^2+{\mathrm{PR}}^2={\mathrm{OP}}^2 \\ \Rightarrow {\mathrm{OR}}^2+{40}^2={41}^2 \\ \Rightarrow {\mathrm{OR}}^2+=1681-1600 \\ \Rightarrow {\mathrm{OR}}^2=81 \\ \Rightarrow \mathrm{OR}=9\mathrm{unit} \end{gathered}$$
Thus, the distance of the chord from the centre of the circle is 9 units.