It is given that AO is angle bisector of angle A and BO is angle bisector of angle B so angle OAP = angle OBP = 45 degrees.
We have OP perpendicular to AB so angle OPB = 90 degrees..
In triangle OPB
angle OBP = 45 degree , angle OPB = 90 degree so angle POB =45 degree.
Two angles of the triangle are equal so the triangle is the isosceles triangle.
OP = PB
Similarly for triangle AOP
OP = AP
Wet OP =AP =PB
OP=AP = AB2
It is not given that AB is length or breadth
OP = AP = 2 or 3
Distance of point O from AB is OP so our answer should be option A and C