A current i flowing through the loop as shown in figure. The magnetic field at the centre O is

The angle, subtended by arc DE at O is $\frac{\pi }{2}$ and by arc FC at $O=\frac{3\pi }{2}$
The effective magnetic field at O is
 $\begin{array}{l}B=B_{DE}+B_{FC}\\ =\frac{{\mu }_0}{4\pi }\frac{i}{3r}.\frac{\pi }{2}+\frac{{\mu }_0}{4\pi }\frac{i}{r}.\frac{3\pi }{2}\\ =\frac{{\mu }_{0}i}{8r}(3+\frac{1}{3})\\ =\frac{5{\mu }_{0}i}{12r}\mathrm{acting}\mathrm{downwards}\end{array}$