## X(1125) (COMPLEMENT OF X(10))

 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.

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

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           (2a+b+c)/a : (a+2b+c)/b : (a+b+2c)/c
Barycentrics    2a+b+c : a+2b+c : a+b+2c

The centroid of four points A,B,C,P is the complement of the complement of P with respect to triangle ABC. As an example, X(1125) is the centroid of {A,B,C,X(1)}. (Darij Grinberg, 12/28/02)

X(1125) lies on these lines:
1,2    3,142    5,515    11,214    21,36    33,475    34,406    35,404    37,39    40,631    55,474    56,226    58,86    65,392    72,354    105,831    114,116    140,517    165,962    171,595    274,350    409,759    443,497    749,984    758,942    958,999    1015,1107

X(1125) is the {X(1),X(2)}-harmonic conjugate of X(10).

X(1125) = midpoint of X(I) and X(J) for these (I,J):
(1,10), (2,551), (3,946), (5,1385), (11,214), (142,1001), (226,993), (942,960)

X(1125) = isogonal conjugate of X(1126)
X(1125) = isotomic conjugate of X(1268)
X(1125) = complement of X(10)
X(1125) = crosspoint of X(2) and X(86)
X(1125) = crosssum of X(6) and X(42)

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