There seems to be a similar question in this exchange:
How could I use the centroid and size of a triangle to find the coordinates of its vertices?
But this one specifies that it has the centroid and the size of the triangle.
In my case what i am trying to do is to calculate the minimum bounding box for a triangle but i only have the following information:
- X, Y coordinates of the center of the triangle
- Length of the each sides.
Can anyone give me a hint? or this is also not possible.
Thx!
The triangle is only determined up to rotations and reflections.
Let $G$ be the centroid of $\triangle ABC$. The length of the medians can be calculated in terms of the sides using the median length formula. That gives the length of $GA$ as $2/3$ the length of the median through $A$. Choose $A$ to be any point on the circle centered at $G$ of radius $GA$. Now construct $B$ knowing the distances $AB,GB\,$, then $C$ the same way. Depending on the choice of $B$ on either side of $GA$ this gives two possible triangles $ABC$ which are reflections of each other.