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 sec(A + ω) : sec(B + ω) : sec(C + ω)
= f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = bc/(b4 + c4 - a2b2 - a2c2)Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = 1/(b4 + c4 - a2b2 - a2c2)
X(98) = circumcircle-antipode of X(99)
X(98) = the point of intersection, other than A, B, and C, of the circumcircle and Kiepert hyperbola.
X(98) = Ψ(X(101), X(100)J. W. Clawson, "Points on the circumcircle," American Mathematical Monthly 32 (1925) 169-174.
X(98) lies on these lines:
2,110 3,76 4,32 5,83 6,262 10,101 13,1080 14,383 20,148 22,925 23,94 25,107 30,671 100,228 109,171 186,935 275,427 376,543 381,598 385,511 468,685 523,842 620,631 804,878X(98) is the {X(2),X(147)}-harmonic conjugate of X(114). For a list of harmonic conjugates, click More at the top of this page.
X(98) = midpoint between X(20) and X(148)
X(98) = reflection of X(I) in X(J) for these (I,J): (4,115), (99,3), (147,114), (1513,230)
X(98) = isogonal conjugate of X(511)
X(98) = isotomic conjugate of X(325)
X(98) = complement of X(147)
X(98) = anticomplement of X(114)
X(98) = X(290)-Ceva conjugate of X(287)
X(98) = cevapoint of X(I) and X(J) for these (I,J): (2,385), (6,237)
X(98) = X(I)-cross conjugate of X(J) for these (I,J): (230,2), (237,6), (248,287), (446,511)
X(98) = crosssum of X(385) and X(401)
X(98) = X(2)-Hirst inverse of X(287)