# Construction of a Triangle from Two Vertices and the Centroid

Jared Brandt has sent me two solutions to the problem of constructing a triangle from two vertices and the centroid. The second one came with a curious commentary. It shows that even after a problem has been solved it pays to have a second look: there may be generalizations or other, simpler solutions.

Hello! I was looking at your page: https://www.cut-the-knot.org/triangle/index.shtml and I have a solution to what seems to be an unanswered problem:

It is as follows:

Given: {A, B, G}

Construct: ABC

- Draw line AB.
- Construct the midpoint of AB, M
_{c}. - Draw the lines M
_{c}G, AG, and BG. - Construct the perpendicular to AG through B and call the intersection between it and AG, P.
- Draw the circle (P, PB) and call the other intersection between it and BP, Q.
- Construct the parallel to AG through Q and call the intersection between it and M
_{c}G, 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

The second solution reached me just a few minutes after the first:

Or you could just be a goof like me and completely overlook the fact that _{c}G,_{c}G at the very beginning, we can quickly find C.

- Jared

Thank you, Jared.

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