HJB --- GMA --- UFF


Click here to access the list of all triangle centers.

Interactive Applet

You can move the points A, B and C (click on the point and drag it).
Press the keys “+” and “−” to zoom in or zoom out the visualization window and use the arrow keys to translate it.

You can also construct all centers related with this one (as described in ETC) using the “Run Macro Tool”. To do this, click on the icon Run Macro Tool, select the center name from the list and, then, click on the vertices A, B and C successively.

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Download all construction files and macros: (10.1 Mb).
This applet was built with the free and multiplatform dynamic geometry software C.a.R..

Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           sin(A - π/3) : sin(B - π/3) : sin(C - π/3)
                                    = cos(A + π/6) : cos(B + π/6) : cos(C + π/6)

Barycentrics    a sin(A - π/3) : b sin(B - π/3) : c sin(C - π/3)

Let U and V be the points on sideline BC met by the interior and exterior bisectors of angle A. The circle having diameter UV is the A-Apollonian circle. The B- and C- Apollonian circles are similarly constructed. Each circle passes through a vertex and both isodynamic points. The pedal triangle of X(16) is equilateral.

X(16) lies on these lines:
1,1250    2,13    3,6    4,18    14,30    17,140    36,203    55,202    299,532    302,316    358,1135    396,549    398,550    533,617    627,635

X(16) is the {X(3),X(6)}-harmonic conjugate of X(15).

X(16) = reflection of X(I) in X(J) for these (I,J): (14,395), (15,187), (299,619), (316,623), (622,624)
X(16) = isogonal conjugate of X(14)
X(16) = isotomic conjugate of X(301)
X(16) = inverse-in-circumcircle of X(15)
X(16) = inverse-in-Brocard-circle of X(15)
X(16) = complement of X(622)
X(16) = anticomplement of X(624)
X(16) = X(I)-Ceva conjugate of X(J) for these (I,J): (1,203), (14,61), (74,15)
X(16) = crosspoint of X(I) and X(J) for these (I,J): (14,17), (299,471)
X(16) = crosssum of X(I) and X(J) for these (I,J): (16,61), (533,618)
X(16) = crossdifference of any two points on line X(396)X(523)
X(16) = X(6)-Hirst inverse of X(15)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.

If you have questions or suggestions, please, contact us using the e-mail presented here.

Departamento de Matemática Aplicada -- Instituto de Matemática -- Universidade Federal Fluminense

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