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 2 + cos(B - C) : 2 + cos(C - A) : 2 + cos(A - B)
Barycentrics (sin A)[2 + cos(B - C)] : (sin B)[2 + cos(C - A)] : (sin C)[2 + cos(A - B)]X(495) is the midpoint of segments C1-to-P1, C2-to-P2, C3-to-P3 in the Johnson four-circle configuration.
Roger A. Johnson, Advanced Euclidean Geometry, Dover, New York, 1960, page 75.
Peter Yff, "Three concurrent congruent circles 'inscribed' in a triangle," manuscript, 1998; X(495) is the point R on page 5. (See also X(496)-X(499) and X(1478), X(1479).)
X(495) lies on these lines:
1,5 2,956 3,388 4,390 8,442 10,141 30,55 35,550 36,549 56,140 202,395 203,396 226,517 381,497 392,908 429,1068 529,993 612,1060