Construction help?

Question

A line segment AB is given. How can we draw a line perpendicular to AB and passing through A with a straight edge and a compass?

Answer 1

with A as centre and any suitable radius draw a semicircle to the left of AB
again with the same radius cut arcs1 and 2
with the points of intersection of the arcs 1 and 2 draw arcs
draw a line through the point of intersection through A
this will be your required perpendicular through A

Answer 2

First, construct a circle with center at A and an arbitrary radius. Mark the two points, C and D, where the circle intersects line AB.

Second, construct a circle with center at C that passes thru D.
Third, construct a circle with center at D that passes thru C.
Mark the two points, E and F, where the circles centered at C and D intersect.
Finally, draw a line thru points E and F. It will also go thru A and be perpendicular to AB.