The magnetic field at the center $P$ is the sum of the fields due to the two straight segments and the semi-circular arc. The field due to the two semi-infinite straight wires at $P$ is $B_{straight} = \frac{\mu_0 i}{4\pi R} + \frac{\mu_0 i}{4\pi R} = \frac{\mu_0 i}{2\pi R}$ (pointing into the page). The field due to the semi-circular arc is $B_{arc} = \frac{\mu_0 i}{4R}$ (pointing out of the page). The net field is $B_{net} = \frac{\mu_0 i}{4R} - \frac{\mu_0 i}{2\pi R} = \frac{\mu_0 i}{4R} [1 - \frac{2}{\pi}]$ pointing out of the page.