Hello! I was looking at your page: http://www.cut-the-knot.org/triangle/index.shtml and I have a solution to what seems to be an unanswered problem: {A, B, G}.

It is as follows:

Given: {A, B, G}
Construct: ABC

1. Draw line AB.
2. Construct the midpoint of AB, M_c.
3. Draw the lines M_cG, AG, and BG.
4. Construct the perpendicular to AG through B and call the intersection between it and AG, P.
5. Draw the circle (P, PB) and call the other intersection between it and BP, Q.
6. Construct the parallel to AG through Q and call the intersection between it and M_cG, C.

You now have all three point, A, B, and C, and can simply connect the dots to get the triangle!

Thanks for reading!
- Jared

Or you could just be a goof like me and completely overlook the fact that CG = 2M_cG, and since you know M_cG at the very beginning, we can quickly find C.

- Jared