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 (b - c)2 - ab - ac : (c - a)2 - bc - ba : (a - b)2 - ca - cb
= 2 + cos B + cos C : 2 + cos C + cos A : 2 + cos A + cos BBarycentrics a[(b - c)2 - ab - ac] : b[(c - a)2 - bc - ba] : c[(a - b)2 - ca - cb]
X(354) is the centroid of the intouch triangle.
William Gallatly, The Modern Geometry of the Triangle, 2nd edition, Hodgson, London, 1913, page 16.
X(354) lies on these lines: 1,3 2,210 6,374 7,479 11,118 37,38 42,244 44,748 48,584 63,1001 81,105 278,955 373,375 388,938 392,551 516,553
X(354) = isogonal conjugate of X(2346)
X(354) = inverse-in-incircle of X(1155)
X(354) = reflection of X(I) in X(J) for these (I,J): (210,2), (392,551)
X(354) = X(101)-Ceva conjugate of X(513)
X(354) = crosspoint of X(1) and X(7)
X(354) = crosssum of X(1) and X(55)