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 f(A,B,C) : f(B,C,A) : f(C,A,B),
where f(A,B,C) = 1/(sin A + 2 cos A)
Barycentrics (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)
To construct the Vecten point, X(485), squares are erected outward on the sides of ABC. If A', B', C' are the centers of these squares, then triangle A'B'C' is perspective to ABC with perspector X(485). Now let A" be the midpoint of the side of the A-square that does not touch line BC, and define B" and C" cyclically. Then triangle A"B"C" is perspective to ABC with perspector X(1131). Angle(A"BC) = angle(B"CA) = angle(C"AB), so that X(1131) lies on the Kiepert hyperbola. Here, the common angle is arctan(2). (Darij Grinberg 9/22/02)
X(1131) lies on these lines: 2,490 6,1132 20,485 175,226
X(1131) = isogonal conjugate of X(1151)
X(1131) = isotomic conjugate of X(1270)