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 1 + 2 sin B sin C : 1 + 2 sin C sin A : 1 + 2 sin A sin B
Barycentrics (sin A)(1 + 2 sin B sin C) : (sin B)(1 + 2 sin C sin A) : (sin C)(1 + 2 sin A sin B)X(498) and X(499) are harmonic conjugate points with respect to X(1) and X(2), in analogy with such pairs with respect to X(1), X(4) and with respect to X(1), X(5).
Peter Yff, "Three concurrent congruent circles 'inscribed' in a triangle," manuscript, 1998; X(498) is the point S on page 6.
X(498) lies on these lines: 1,2 3,12 4,35 5,55 9,920 36,388 37,91 46,226 47,171 56,140 141,611 191,329 255,750 345,1089