## X(41) (X(6)-CEVA CONJUGATE OF X(31))

 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.

 The JRE (Java Runtime Environment) is not enabled in your browser!

This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           a2(b + c - a) : b2(c + a - b) : c2(a + b - c)
= a2cot(A/2) : b2cot(B/2) : c2cot(C/2)

Barycentrics    a3(b + c - a) : b3(c + a - b) : c3(a + b - c)

X(41) lies on these lines: 1,101    3,218    6,48    9,21    25,42    31,32    37,584    55,220    58,609    65,910    219,1036    226,379    560,872    601,906    603,911    663,884

X(41) is the {X(32),X(213)}-harmonic conjugate of X(31).

X(41) = isogonal conjugate of X(85)
X(41) = X(I)-Ceva conjugate of X(J) for these (I,J): (6,31), (9,212), (284,55)
X(41) = crosspoint of X(I) and X(J) for these (I,J): (6,55), (9,33)
X(41) = crosssum of X(I) and X(J) for these (I,J): (1,169), (2,7), (57,77), (92,342), (226,1441), (514,1111)
X(41) = crossdifference of any two points on line X(522)X(693)
X(41) = X(I)-beth conjugate of X(J) for these (I,J): (41,32), (101,41), (220,220)

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