INSTITUTO DE MATEMÁTICA
HJB --- GMA --- UFF

X(399)
(PARRY REFLECTION POINT)


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: tc.zip (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           f(A,B,C) : f(B,C,A) : f(C,A,B), where
                                    f(A,B,C) = 5 cos A - 4 cos B cos C - 8 sin B sin C cos2A

Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,B,A)

Let L, M, N be lines through A, B, C, respectively, parallel to the Euler line. Let L' be the reflection of L in sideline BC, let M' be the reflection of M in sideline CA, and let N' be the reflection of N in sideline AB. The lines L', M', N' concur in X(399).

Cyril Parry, Problem 10637, American Mathematical Monthly 105 (1998) 68.

X(399) lies on these lines:
3,74    4,195    6,13    30,146    155,382    394,541

X(399) = isogonal conjugate of X(1138)
X(399) = reflection of X(I) in X(J) for these (I,J): (3,110), (74,1511), (265,113)
X(399) = X(I)-Ceva conjugate of X(J) for these (I,J): (30,3), (323,6)

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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