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 cos A sin2(B - C) : cos B sin2(C - A) : cos C sin2(A - B)
= (sec A)(c cos C - b cos B)2 : (sec B)(a cos A - c cos C)2 : (sec C)(b cos B - a cos A)2
= bc(b2 + c2 - a2)(b2 - c2)2 : ca(c2 + a2 - b2)(c2 - a2)2 : ab(a2 + b2 - c2)(a2 - b2)2Barycentrics (sin 2A)[sin(B - C)]2 : (sin 2B)[sin(C - A)]2 : (sin 2C)[sin(A - B)]2
X(125) lies on the nine-point circle
X(125) = X(110)-of-medial triangle
X(125) = X(100)-of-orthic triangle, if ABC is acute
Roland H. Eddy and R. Fritsch, "The conics of Ludwig Kiepert: a comprehensive lesson in the geometry of the triangle," Mathematics Magazine 67 (1994) 188-205.
X(125) lies on these lines:
2,98 3,131 4,74 5,113 6,67 51,132 68,1092 69,895 115,245 119,442 122,684 126,141 128,140 136,338 381,541 511,858X(125) = midpoint of X(I) and X(J) for these (I,J): (3,265), (4,74), (6,67)
X(125) = reflection of X(I) in X(J) for these (I,J): (113,5), (185,974), (1495,468), (1511,140), (1539,546)
X(125) = isogonal conjugate of X(250)
X(125) = inverse-in-Brocard-circle of X(184)
X(125) = complement of X(110)
X(125) = complementary conjugate of X(523)
X(125) = X(I)-Ceva conjugate of X(J) for these (I,J): (4,523), (66,512), (68,520), (69,525), (338,115)
X(125) = crosspoint of X(I) and X(J) for these (I,J): (4,523), (69,525), (338,339)
X(125) = crosssum of X(I) and X(J) for these (I,J): (3,110), (25,112), (162,270), (1113,1114)
X(125) = crossdifference of any two points on line X(110)X(112)
X(125) = X(115)-Hirst inverse of X(868)
X(125) = X(2)-line conjugate of X(110)