(a)AO=OC (radii)
arc AO= arc OC (equal chords, equal arcs)
so angle ABO = OBC ( arcs prop to angles at circumference)
so OB bisects angle ABC
(b) angle AOC=90 degree ( angle in semi circle)
angle ABC+ angle AOC=180 degree ( opp angles of cyclic quad)
So angle ABC = 90 degree
Since OB is the angle bisector,
2 angle ABO= 90 degree
So angle ABO=45 degree