Question

The radius of a circle with centre O is 41 the length of the chord PQ of same circle is 80. Determine the distance of chord PQ from centre O.

Answer 1

Let the radii OP = OQ = 41 cm.
We draw a perpendicular OM from the centre O on the chord PQ.
We know that perpendicular from the centre bisects the chord.
Therefore, PM = MQ = $\frac{80}{2}=40$ cm

$$\begin{gathered} \mathrm{And}\angle \mathrm{OMP}=\angle \mathrm{OMQ}=90° \\ \mathrm{Now}\mathrm{in}\mathrm{right}△\mathrm{OMP}, \\ \mathrm{OM}\hspace{0.17em}=\sqrt{{\mathrm{OP}}^2-{\mathrm{PM}}^2} \\ =\sqrt{{41}^2-{40}^2} \\ =\sqrt{1681-1600} \\ =\sqrt{81} \\ =9\mathrm{cm} \\ \therefore \mathrm{Distance}\mathrm{of}\mathrm{the}\mathrm{chord}\mathrm{PQ}\mathrm{from}\mathrm{the}\mathrm{centre}\mathrm{O}=9\mathrm{cm}. \end{gathered}$$