Using straightedge only, construct perpendicular line to diameter AB of a given circle through given point C?

Question

Someone drawn a circle on a piece of paper, marked its dimater AB, and took away the compass.

http://i4.tinypic.com/53jpr1l.gif

Answer 1

Draw the lin AC intersecting the circle at Point D.
Draw a line from C to B and extend it until it intersects the circle at the point E.
Draw the line AE and extend it so that it will intersect the line DB extended at the point F. Draw CF intersecting the line AB at G. Then CF is perpendicular to AB at G

Q.E.F

Answer 2

NO compass? I don't know how much you could actually do then. The following isn't a proof but maybe this will give somebody some ideas:

Use the straightedge to draw AC abd BC, Let "d" be the point on the circle where it intersects AC. Since AB is a diameter, angle AdB is a right angle. Draw dB and extend it past the point underneath C. From there, I still don't know what else you could do to draw the perpendicular line. All I can think of is that it has something to do with the circle.

Answer 3

It's doable, I know that, because there is a theorem which says that any construction which can be done with a straightedge and compass can be done with a straightedge alone if you are given only an arc of *any* circle.

But the straight-edge alone constructions are quite painful, so that doesn't help for this specific case.

Answer 4

Ask for the compass back. You're gonna need it. You need to find the center of the circle, which is the midpoint of AB...and, to do that, you'll need the compass.