How do I construct the circumcenter and incenter of an equilateral triangle using a ruler and compass? HELP!?

Answer 1

It's easy to do, but pretty difficult to explain over just typing....

Let's say you have a triangle ABC.

Let's take just a segment AB. Put your compass needle on point A and adjust the width of yoru compass to be more than half of AB but less than full AB. Now, write an arc over the segment AB. Make sure it is long enough. You'll see the reason on the next step. Now, put your needle on point B. Do the same over the same segment AB. Now you have two overlapping arcs that sort of look like an eye shape. If you made the arcs long enough, they cross each other, correct? Use a ruler and put a line through the points where they cross each other. This line, which intersects the segment AB, is EXACTLY crossing the half way point of the segment AB.

NOW, use your ruler and put a line through the half way opint of AB to the point C.

Repeat the above process for segment BC, and CA.

What you end up is 3 lines crossing each other at the center of the triangle. That's your center. You can figure out the rest.

Answer 2

The circumcenter will be where the three perpendicular bisectors of the sides meet. The incenter is where the three angle bisectors of the angles meet.

Explaining a construction so that you may construct it is rather tedious. Way to go TK!