Golden triangle (mathematics) Golden triangle (mathematics) A golden triangle, also known as the sublime triangle,is an isosceles triangle in which the duplicated side is in the golden ratio to the distinct side: Golden triangles are found in the nets of several stellations of dodecahedrons and icosahedrons. Also, it is the shape of the triangles found in the points of pentagrams. The vertex angle is equal to Since the angles of a triangle sum to 180°, base angles are therefore 72° each. The golden triangle can also be found in a regular decagon, or an equiangular and equilateral ten-sided polygon, by connecting any two
Incircle and excircles of a triangle any vertex to the incircle tangency on either adjacent side is half the sum of the vertex's adjacent sides minus half the opposite side. Thus for example for vertex "B" and adjacent tangencies "T" and "T", The incircle radius is no greater than one-ninth the sum of the altitudes. The squared distance from the incenter "I" to the circumcenter "O" is given by and the distance from the incenter to the center "N" of the nine point circle is The incenter lies in the medial triangle (whose vertices are the midpoints of the sides). The radius of the incircle is