Morley's trisector theorem (area)

Description

Morley’s trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the first Morley triangle or simply the Morley triangle. (For a positive integer N, an angle of measure 2π/N is trisectible if and only if 3 does not divide N . The first Morley triangle has area related to the circumradius of the original triangle and the angles of the original triangle.

Related formulas

Variables

AMorleyThe area of the Morley’s triangle (m2)
RThe circumradius of the original triangle (m)
AThe angle of the original triangle opposite to side a (radians)
BThe angle of the original triangle opposite to side b (radians)
CThe angle of the original triangle opposite to side c (radians)