Question

If chord PQ of a circle have length equal to the radius then find the distance of chord from centre in terms of radius.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{OP}=\mathrm{OQ}=r. \\ \mathrm{Now},\mathrm{PQ}\mathrm{is}\text{the}\mathrm{chord}\mathrm{which}\mathrm{is}\mathrm{equal}\mathrm{to}\mathrm{radius}. \\ \therefore \mathrm{PQ}=r. \\ \mathrm{OM}\mathrm{is}\text{the}\mathrm{distance}\mathrm{of}\mathrm{chord}\mathrm{from}\mathrm{centre}\mathrm{O}. \\ \therefore \mathrm{OM}\perp \mathrm{PQ}. \\ \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{pependicular}\mathrm{from}\mathrm{the}\mathrm{centre}\mathrm{on}\mathrm{the}\mathrm{chord}\mathrm{divides}\mathrm{the}\mathrm{chord}. \\ \therefore \mathrm{PM}=\mathrm{MQ}=\frac{r}{2} \\ \mathrm{Now},\mathrm{in}\mathrm{right}△\mathrm{OPM}, \\ \mathrm{OM}=\sqrt{{\mathrm{OP}}^2-{\mathrm{PM}}^2} \\ =\sqrt{r^2-{\left({\displaystyle \frac{r}{2}}\right)}^2} \\ =\sqrt{r^2-\frac{r^2}{4}} \\ =\frac{\sqrt{3}}{2}r \end{gathered}$$