Integer triangle common divisor. Integer triangles with a 60° angle can also be generated by with coprime integers "m", "n" with 0 < "n" < "m" (the angle of 60° is opposite to the side of length "a"). From here, all primitive solutions can be obtained by dividing "a", "b", and "c" by their greatest common divisor (e.g. an equilateral triangle solution is obtained by taking "m" = 2 and "n" = 1, but this produces "a" = "b" = "c" = 3, which is not a primitive solution). See also More precisely, If formula_109, then formula_110, otherwise formula_111. Two different pairs
Integer triangle harmonic progression. This is because such angles have to be rational angles of the form with rational 0 < < 1. But all the angles of integer triangles must have rational cosines and this will occur only when = i.e. the integer triangle is equilateral. The square of each internal angle bisector of an integer triangle is rational, because the general triangle formula for the internal angle bisector of angle "A" is formula_2 where "s" is the semiperimeter (and likewise for the other angles' bisectors). Any altitude dropped from a vertex onto an opposite side or its extension will split