One side

By: Tim Lehman

Given:

Construction:

First, construct the median to side **b**.
We know vertices **A** and **C** are on the circle centered
at the midpoint of side **b** with a radius of a half of length
**b**. Because the centroid cuts the medians in a 2 to 1 ratio,
the vertex **A** is on the circle centered at the centroid
with a radius of 2/3 the length of the median to side **a**.
The vertex **A** is at the intersection of these two circles.
Vertex **C** can be found because it is on the line through
vertex **A** and the midpoint of side **b** and on the first
circle drawn.

**Click here** for a GSP sketch of the above construction.