${{\text{B}}_{\text{B}}} = \frac{{{\mu _0}}}{{4\pi }}\frac{{(2\pi  - \pi /2){\text{I}}}}{{\text{r}}} \otimes $

$ = \frac{{{\mu _0}}}{{4\pi }}\frac{{3\pi {\text{I}}}}{{2{\text{r}}}}$

$\mathrm{B}_{\mathrm{C}}=\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{r}} \otimes $

So, net magnetic field at the centre $=\mathrm{B}_{\mathrm{A}}+\mathrm{B}_{\mathrm{B}}+\mathrm{B}_{\mathrm{C}}$

$=0+\frac{\mu_{0}}{4 \pi} \frac{3 \pi \mathrm{I}}{2 \mathrm{r}}+\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{r}}=\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{r}}\left(\frac{3 \pi}{2}+1\right)$