Acute and obtuse triangles "x", then If two obtuse triangles have sides ("a, b, c") and ("p, q, r") with "c" and "r" being the respective longest sides, then The Calabi triangle, which is the only non-equilateral triangle for which the largest square that fits in the interior can be positioned in any of three different ways, is obtuse and isosceles with base angles 39.1320261...° and third angle 101.7359477...°. The equilateral triangle, with three 60° angles, is acute. The Morley triangle, formed from any triangle by the intersections of its adjacent angle trisectors, is equilateral and hence acute. The golden triangle is the isosceles
Incircle and excircles of a triangle Because the Incenter is the same distance of all sides the trilinear coordinates for the incenter are The barycentric coordinates for a point in a triangle give weights such that the point is the weighted average of the triangle vertex positions. Barycentric coordinates for the incenter are given by where formula_7, formula_8, and formula_9 are the lengths of the sides of the triangle, or equivalently (using the law of sines) by where formula_11, formula_12, and formula_13 are the angles at the three vertices. The Cartesian coordinates of the incenter are a weighted average of the coordinates of the three vertices