Integer triangle formula_112 and formula_113 generate the same triple. Unfortunately the two pairs can both be of gcd=3, so we can't avoid duplicates by simply skipping that case. Instead, duplicates can be avoided by formula_27 going only till formula_115. Note that we still need to divide by 3 if gcd=3. The only solution for formula_116 under the above constraints is formula_117 for formula_118. With this additional formula_119 constraint all triples can be generated uniquely. An Eisenstein triple is a set of integers which are the lengths of the sides of a triangle where one of the angles is 60 degrees. Integer triangles
Bisection The interior angle bisectors of a triangle are concurrent in a point called the incenter of the triangle, as seen in the diagram at right. The bisectors of two exterior angles and the bisector of the other interior angle are concurrent. Three intersection points, each of an external angle bisector with the opposite extended side, are collinear (fall on the same line as each other). Three intersection points, two of them between an interior angle bisector and the opposite side, and the third between the other exterior angle bisector and the opposite side extended, are collinear. The angle bisector theorem