In the given figure, a circle centred at origin O has radius $\displaystyle 7 \mathrm{~cm}, \mathrm{OC}$ is median of $\displaystyle \Delta \mathrm{OAB}$. Find the length of median OC.

\[\begin{aligned} & \angle \mathrm{AOB}=90^{\circ} \\ & \therefore \mathrm{AB}{ }^{2}=7^{2}+7^{2} \\ & \Rightarrow \mathrm{AB}=7 \sqrt{2} \mathrm{~cm} \\ & \Rightarrow \mathrm{AC}=\frac{7 \sqrt{2}}{2} \mathrm{~cm} \\ & \text { Now In } \Delta \mathrm{AOC}, \\ & \Rightarrow \mathrm{OC}^{2}=7^{2}-\left(\frac{7 \sqrt{2}}{2}\right)^{2} \\ & \therefore \mathrm{OC}=\frac{7 \sqrt{2}}{2} \mathrm{~cm} \end{aligned} \] \[\begin{aligned} & \Rightarrow \mathrm{OC}^{2}=7^{2}-\left(\frac{7 \sqrt{2}}{2}\right)^{2} \\ & \therefore \mathrm{OC}=\frac{7 \sqrt{2}}{2} \mathrm{~cm} \end{aligned} \]