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) = a[a^{3} - b^{3} - c^{3} - bc(a + b + c) + ab(a - b) + ac(a - c)]/(b + c)Barycentrics af(a,b,c) : bf(b,c,a) : cf(c,a,b)
Miquel's theorem states that if A', B', C' are points (other than A, B, C) on sidelines BC, CA, AB, respectively, then the circles AB'C', BC'A', CA'B' meet at a point. Suppose P is a point and A' = P∩BC, B' = P∩CA, C' = P∩AB; the point in which the three circles is the Miquel associate of P. (Paul Yiu, 7/6/99)
X(501) lies on these lines: 1,229 10,662 21,214 35,110 36,58 215,1364 284,942 572,992 595,1326 759,1385
X(501) = isogonal conjugate of X(502)