Integer triangle side of the formula are integers it follows that all integer triangles must have an integer value of "16T" and "T" will be rational. By the law of cosines, every angle of an integer triangle has a rational cosine. If the angles of any triangle form an arithmetic progression then one of its angles must be 60°. For integer triangles the remaining angles must also have rational cosines and a method of generating such triangles is given below. However, apart from the trivial case of an equilateral triangle there are no integer triangles whose angles form either a geometric or
Integer triangle inequality. An important characteristic of the automedian triangle is that the squares of its sides form an arithmetic progression. Specifically, formula_91 so formula_92. A triangle family with integer sides formula_93 and with rational bisector formula_94 of angle A is given by with integers formula_99. There exist infinitely many non-similar triangles in which the three sides and the bisectors of each of the three angles are integers. There exist infinitely many non-similar triangles in which the three sides and the two trisectors of each of the three angles are integers. However, for "n" > 3 there exist no triangles in which