Law of cosines . The power of the point with respect to the circle is equal to both and . Therefore, which is the law of cosines. Using algebraic measures for line segments (allowing negative numbers as lengths of segments) the case of obtuse angle () and acute angle () can be treated simultaneously. By using the law of sines and knowing that the angles of a triangle must sum to 180 degrees, we have the following system of equations (the three unknowns are the angles): Then, by using the third equation of the system, we obtain a system of two equations in
Triangle angles is equal to 90°, adding up to a total of 270°. Specifically, on a sphere the sum of the angles of a triangle is where "f" is the fraction of the sphere's area which is enclosed by the triangle. For example, suppose that we draw a triangle on the Earth's surface with vertices at the North Pole, at a point on the equator at 0° longitude, and a point on the equator at 90° West longitude. The great circle line between the latter two points is the equator, and the great circle line between either of those points and