In the figure, what is the magnitude of magnetic induction at centre of semicircle point O ?

Due to segment lthe magnetıc field at the point O is zero because the point lies on the axis of the wire segment 1 . So B₁ = 0 Segment 2 is in the shape of a semi circle. The magnetic field at point O due to the semicircle is given by ${\mathrm{B}}_2=\frac{{\mathrm{\mu }}_0\mathrm{I}}{4\mathrm{r}}.$
The magnetic field at point O due to segment 3 is same as the magnetic field due to a semi infinite wire. So the magnetic field due to segment 3 at point O is ${\mathrm{B}}_3=\frac{{\mathrm{\mu }}_0\mathrm{I}}{4\mathrm{\pi r}}$.
If we move along the wire and use the right hand thumb rule for each of the segment, we will know that the direction of magnetic field at point O is outwards. Hence, the net magnetic field at the point O is

${\mathrm{B}}_{\mathrm{net}}={\mathrm{B}}_1+{\mathrm{B}}_2+{\mathrm{B}}_3=\frac{{\mathrm{\mu }}_0\mathrm{I}}{4\mathrm{r}} +\frac{{\mathrm{\mu }}_0\mathrm{I}}{4\mathrm{\pi r}}$