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 , select the center name from the list and, then, click on the vertices A, B and C successively.
Information from Kimberling's Encyclopedia of Triangle Centers |
(CONGRUENT PARALLELIANS POINT) Trilinears bc(ca + ab - bc) : ca(ab + bc - ca) : ab(bc + ca - ab)
Barycentrics ca + ab - bc : ab + bc - ca : bc + ca - abSegments through X(192) parallel to the sidelines with endpoints on the sidelines have equal length. For references as early as 1881, see Hyacinthos message 2929 (Paul Yiu, May 29, 2001). See also
Sabrina Bier, "Equilateral Triangles Intercepted by Oriented Parallelians," Forum Geometricorum 1 (2001) 25-32.
X(192) lies on these lines:
1,87 2,37 6,190 7,335 8,256 9,239 55,385 69,742 144,145 315,746 869,1045X(192) = reflection of X(I) in X(J) for these (I,J): (8,984), (75,37), (1278,75)
X(192) = isogonal conjugate of X(2162)
X(192) = isotomic conjugate of X(330)
X(192) = complement of X(1278)
X(192) = anticomplement of X(75)
X(192) = X(1)-Ceva conjugate of X(2)
X(192) = crosspoint of X(1) and X(43)
X(192) = crosssum of X(1) and X(87)
X(192) = X(9)-Hirst inverse of X(239)
X(192) = X(646)-beth conjugate of X(192)