Any other circle is a small circle 2. Agreat!many!spherical!triangles!can!be!solved!using!these!two!laws,!but!unlike!planar! The rules are aided with the Napier’s circle. Consider the following generalization of this construction. (a) If AB = AC are the base angles at B and C equal? 8 Properties of spherical triangle : 1. If equilateral triangles are constructed outwards or inwards on the sides of any given triangle, then the centroids of these triangles are the vertices of an equilateral triangle. Let d(.,.) Solution of right spherical triangle With any two quantities given (three quantities if the right angle is counted), any right spherical triangle can be solved by following the Napier’s rules. Yes (b) If the angles at B and C are equal is it true that AB = AC? 4. triangles,!some!require!additional!techniques!knownas!the!supplemental! In elementary Euclidean geometry this result is known as Napoleon's Theorem. In a spherical triangle ABC do the following properties hold? The length of the arc of a circle can be measured by the angle which the arc subtends at the center of the circle . A spherical triangle is a triangle each of whose sides is a great circle . If a circle is drawn on a sphere so that the radius of the circle is the same as the radius of the sphere it is called a great circle.