The magnitude of magnetic induction at mid-point O due to current...

The magnetic field at point $O$ due to the two semi-infinite portions of both wires lying along line $BE$ will be $0$.

Using right-hand rule, it can be determined that the magnetic field due to both the semi-infinite portions of wires $BC\text{and}ET$ which are perpendicular to $BE$ will be outwards from the plane.

The magnetic field due to one such portion will be:

$B = \dfrac{{\mu}_{0}I}{4\pi\left(\dfrac{a}{2}\right)}$

Since the magnetic field of both the portions is in same direction, the net magnetic field at $O$ will be:

${B}_{net} = 2 \times \dfrac{{\mu}_{0}I}{4\pi\left(\dfrac{a}{2}\right)} = \dfrac{{\mu}_{0}I}{\pia}$