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(B - C) : sec(C - A) : sec(A - B)
Barycentrics sin A sec(B - C) : sin B sec(C - A) : sin C sec(A - B)
John Rigby, "Brief notes on some forgotten geometrical theorems," Mathematics and Informatics Quarterly 7 (1997) 156-158.
Let O be the circumcenter of triangle ABC, and Oa the circumcenter of triangle BOC. Define Ob and Oc cyclically. Then the lines AOa, BOb, COc concur in X(54). For details and generalization, see
Darij Grinberg, A New Circumcenter Question
X(54) lies on these lines:
2,68 3,97 4,184 5,49 6,24 12,215 36,73 39,248 51,288 64,378 69,95 71,572 72,1006 74,185 112,217 140,252 156,381 186,389 276,290 575,895 826,879X(54) is the {X(5),X(49)}-harmonic conjugate of X(110).
X(54) = midpoint of X(3) and X(195)
X(54) = reflection of X(195) in X(1493)
X(54) = isogonal conjugate of X(5)
X(54) = isotomic conjugate of X(311)
X(54) = inverse-in-circumcircle of X(1157)
X(54) = complement of X(1210)
X(54) = anticomplement of X(1209)
X(54) = X(I)-Ceva conjugate of X(J) for these (I,J): (95,97), (288,6)
X(54) = cevapoint of X(6) and X(184)
X(54) = X(I)-cross conjugate of X(J) for these (I,J): (3,96), (6,275), (186,74), (389,4), (523,110)
X(54) = crosspoint of X(95) and X(275)
X(54) = crosssum of X(I) and X(J) for these (I,J): (3,195), (51,216), (627,628)