Let us take the two triangles ΔBDA and ΔBDC. These two are congruent as:
DA = DC (as BD is bisecting AC), DB is common, and the
Angle BDA = angle BDC = 90 (BD perpendicular to AC)
So It is easy now that: angle DBA = angle DBC
Since their sum is the angle ABC = 90 deg (given),
Hence angle DBC = 1/2 angle ABC. = 45 deg.
Ratio = 1/2