First you should pick any point, let's name it B on the line b.

Construct your first circle with center A and radius AB. . (circle 1 black).Name the intersction between the circle and line given C.

Draw a new circle with center C through A.(circle 2-red)

Add circle 3(green) center B, through A. Mark the intersection of the red and green circles with D.

Join A and D , and you have your perpendicular.