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 |
Trilinears (2a+b+c)/a : (a+2b+c)/b : (a+b+2c)/c
Barycentrics 2a+b+c : a+2b+c : a+b+2cThe 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 1015,1107X(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)