Using only a compass and a straightedge, what construction can ALWAYS be done by using a compass only twice? Using only a compass and a straightedge, what construction can ALWAYS be done by using a compass ONLY TWICE. ?

You can clearly make a equilateral triangle. Indeed just make a circonference. After that, draw a straight line through the origin with the straightedge. You will find a diameter which intersects the circonference in two points. Put the compass in one of those two points, with the drawing bit of the compass at the center of the circle. Hence draw half of a cinconference and it will intersect the circle in two points. Connecting these two points with the point opposite to where you pointed your compass, will give you the triangle.

Triangle with compass

![Triangle Photo](

Another way, which is the typical way used by graphic students (or engineers) is the following: ![Triangle - Easier](