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Without loss of generality, one vertex can be at (0,1).
The distance of each of the other two points from the vertex, and the equality of the distances from each other, yield four equations, in the four unknowns of two x coordinates and two y coordinates.
When these are solved, and the other vertices are placed at (sqrt(27)/2, 3/2) and (sqrt(3),-1), the conditions are met and the length of each side is sqrt(7). |
