Circumhyperbola

Author

Eric W. Weisstein
January 2, 2005

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

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

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

Incident Points

IncidentCenters[KimberlingCenters,ToSidelengths[Conic[{Sequence@@IdentityMatrix[3],Sequence@@(Trilinears/@{Orthocenter,X[1]})}]]]//Timing

IncidentCenters[KimberlingCenters,ToSidelengths[Conic[{Sequence@@IdentityMatrix[3],Sequence@@(Trilinears/@{Orthocenter,X[2]})}]]]//Timing

IncidentCenters[KimberlingCenters,ToSidelengths[Conic[{Sequence@@IdentityMatrix[3],Sequence@@(Trilinears/@{Orthocenter,X[3]})}]]]//Timing

IncidentCenters[KimberlingCenters,ToSidelengths[Conic[{Sequence@@IdentityMatrix[3],Sequence@@(Trilinears/@{Orthocenter,X[5]})}]]]//Timing

Simplify[ToSidelengths[Conic[{Sequence@@IdentityMatrix[3],Sequence@@(Trilinears/@{Orthocenter,X[5]})}]/.Sec[x_]:>TrigExpand[Sec[x]]/.Cos[x_]:>TrigExpand[Cos[x]]],TriangleQ[]]

Factor[%]

Factor[Center[((a^7) b α β-3 (a^5) (b^3) α β+3 (a^3) (b^5) α β-a (b^7) α β-(a^5) b (c^2) α β+a (b^5) (c^2) α β-(a^7) c α γ+(a^5) (b^2) c α γ+3 (a^5) (c^3) α γ-3 (a^3) (c^5) α γ-a (b^2) (c^5) α γ+a (c^7) α γ-(a^2) (b^5) c β γ+(b^7) c β γ-3 (b^5) (c^3) β γ+(a^2) b (c^5) β γ+3 (b^3) (c^5) β γ-b (c^7) β γ)]]

IncidentCenters[KimberlingCenters,%18]//Timing

CenterName[X[137]]

CenterName[X[110]]