Morley's Trisector Theorem - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Math Apps : Algebra and Geometry : Geometry : MathApps/MorleysTrisectorTheorem

Morley's Trisector Theorem

Main Concept

Morley's trisector theorem claims that in any triangle, the points of intersection of the adjacent triangle trisectors form an equilateral triangle. This theorem was discovered in 1899 by Frank Morley. Many proofs of Morley's theorem have been developed, and while the proofs are often technical, an interesting result that arises from the proof is the following equation for the side length of the equilateral triangle that is formed:

 

side length=8 R sinA3sinB3sinC3

 

where A, B, and C are the angles of the larger triangle, and R is the radius of the circumcircle.

 

Use the sliders to visually verify Morley's theorem for different shapes of triangles.

 

 

More MathApps

MathApps/AlgebraAndGeometry