Construction #9
Tangent line to a circle from a point in the exterior of the circle
To see a video of Mr. Ochs doing examples
Mr Ochs Video To see and example done in flash click on a link below Math Open Ref Math is Fun 

Given a line and a point on the line, construct the perpendicular to the line at the given point.
Construct the perpendicular bisector of the line l at point A.
1) Choose a radius for the compass. (usually about 1 inch or so will work)
2) With this radius place the pointer on point A and strike 2 arcs, one on either side of A, which intersects line l to form a new segment XY.
(at this point you are going to do construction #4 to bisect the segment XY and draw the perpendicular that will pass through point A, which is the midpoint of segment XY)
1) Choose a radius for the compass that is larger than ½ the segment.
2) With this radius place your compass pointer on one endpoint of the segment and strike a semicircle(1/2 circle) that passes through the segment.
3) Keeping the same radius, repeat step 2 with the pointer on the other endpoint of the segment. The two semicircles will intersect.
4) With a straight edge draw a line through the points of intersection created by the arcs in steps 2 and 3.
Construct the perpendicular bisector of the line l at point A.
1) Choose a radius for the compass. (usually about 1 inch or so will work)
2) With this radius place the pointer on point A and strike 2 arcs, one on either side of A, which intersects line l to form a new segment XY.
(at this point you are going to do construction #4 to bisect the segment XY and draw the perpendicular that will pass through point A, which is the midpoint of segment XY)
1) Choose a radius for the compass that is larger than ½ the segment.
2) With this radius place your compass pointer on one endpoint of the segment and strike a semicircle(1/2 circle) that passes through the segment.
3) Keeping the same radius, repeat step 2 with the pointer on the other endpoint of the segment. The two semicircles will intersect.
4) With a straight edge draw a line through the points of intersection created by the arcs in steps 2 and 3.