Triangle the North Pole is a line of longitude; so there are right angles at the two points on the equator. Moreover, the angle at the North Pole is also 90° because the other two vertices differ by 90° of longitude. So the sum of the angles in this triangle is . The triangle encloses 1/4 of the northern hemisphere (90°/360° as viewed from the North Pole) and therefore 1/8 of the Earth's surface, so in the formula ; thus the formula correctly gives the sum of the triangle's angles as 270°. From the above angle sum formula we can also
Triangle center if the trilinear coordinates of P can be expressed in the form f(A) : f(B) : f(C) where f(A) is a function of the angle A alone and does not depend on the other angles or on the side lengths. A triangle center P is called a "transcendental triangle center" if P has no trilinear representation using only algebraic functions of a, b and c. Let "f" be a triangle center function. If two sides of a triangle are equal (say "a" = "b") then so two components of the associated triangle center are always equal. Therefore all triangle centers