Exact Trilinear Coordinates

Author

Eric W. Weisstein
February 1, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/ExactTrilinearCoordinates.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/ExactTrilinearCoordinates.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<PlaneGeometry`

Conversion

FullSimplify[ExactTrilinears[{α,β,γ}]]

Centers

Circumradius[{a,b,c}]

Circumcenter

FullSimplify[R First[DistanceTrilinears[FullSimplify[ExactTrilinears[Circumcenter]]]]/Circumradius[{a,b,c}]]

Incenter

FullSimplify[First[DistanceTrilinears[FullSimplify[ExactTrilinears[Incenter]]]]Circumradius[{a,b,c}]]/R

Orthocenter

R FullSimplify[First[DistanceTrilinears[FullSimplify[ExactTrilinears[Orthocenter]]]/Circumradius[{a,b,c}]]]

Symmedian Point

FullSimplify[Circumradius[{a,b,c}]First[DistanceTrilinears[FullSimplify[ExactTrilinears[SymmedianPoint]]]]]/R

Triangle Centroid

FullSimplify[First[DistanceTrilinears[FullSimplify[ExactTrilinears[Centroid]]]]Circumradius[{a,b,c}]]/R