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) = (b + c - 2a)/ (b + c - a)
= g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = 2 - 2 cos A - cos B - cos C (Peter J. C. Moses)Barycentrics af(a,b,c) : bf(b,c,a) : cf(c,a,b)
Let X'Y'Z' be the pedal triangle of the Bevan point, W = X(40); then X(1319) is the point, other than W, in which the circles AWX', BWY', CWZ' concur. (Floor van Lamoen, Hyacinthos #6321, 6352).
X(1319) lies on these lines:
1,3 11,515 12,1125 37,604 44,1317 48,1108 59,518 73,1104 77,1122 106,1168 108,953 210,956 214,519 226,535 355,499 392,993 513,663 529,908 840,934 910,1055 961,1255X(1319) is the {X(1),X(56)}-harmonic conjugate of X(65).
X(1319) = midpoint of X(1) and X(36)
X(1319) = reflection of X(1155) in X(36)
X(1319) = isogonal conjugate of X(1320)
X(1319) = inverse-in-circumcircle of X(56)
X(1319) = inverse-in-incircle of X(65)
X(1319) = cevapoint of X(902) and X(1404)
X(1319) = crosspoint of X(1) and X(104)
X(1319) = crosssum of X(1) and X(517)
X(1319) = crossdifference of any two points on line X(9)X(650)