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 csc(B - C) : csc(C - A) : csc(A - B)
= a/(b2 - c2) : b/(c2 - a2) : c/(a2 - b2)Barycentrics a2/(b2 - c2) : b2/(c2 - a2) : c2/(a2 - b2)
X(110) - circumcircle-antipode of X(74)
X(110) = isogonal conjugate of the isotomic conjugate of X(99)
X(110) = Ψ(X(6), X(3))
X(110) = Feuerbach point of the tangential triangle.J. W. Clawson, "Points on the circumcircle," American Mathematical Monthly 32 (1925) 169-174.
Roland H. Eddy and R. Fritsch, "The conics of Ludwig Kiepert: a comprehensive lesson in the geometry of the triangle," Mathematics Magazine 67 (1994) 188-205.
Benedetto Scimemi, "Paper-folding and Euler's Theorem Revisited," Forum Geometricorum.
Scimemi proves that if the Euler line is reflected in every side of triangle ABC, then the three reflections concur in X(110).
X(110) lies on these lines:
1,60 2,98 3,74 4,113 5,49 6,111 11,215 20,146 21,104 22,154 23,323 24,155 27,917 28,915 30,477 31,593 32,729 39,755 58,106 65,229 67,141 69,206 81,105 86,675 97,418 99,690 100,643 101,163 102,283 107,648 108,162 143,195 187,352 190,835 249,512 250,520 251,694 274,767 324,436 351,526 353,574 373,575 376,541 476,523 525,935 560,715 595,849 668,839 669,805 670,689 681,823 685,850 789,799 859,953X(110) is the {X(5),X(49)}-harmonic conjugate of X(54).
X(110) = midpoint of X(I) and X(J) for these (I,J): (3,399), (20,146), (23,323)
X(110) = reflection of X(I) in X(J) for these (I,J): (3,1511), (4,113), (23,1495), (67,141), (74,3), (265,5), (382,1539), (895,6), (1177,206)X(110) = isogonal conjugate of X(523)
X(110) = isotomic conjugate of X(850)
X(110) = inverse of X(2) in the Brocard circle
X(110) = anticomplement of X(125)
X(110) = X(I)-Ceva conjugate of X(J) for these (I,J): (249,6), (250,3)
X(110) = cevapoint of X(I) and X(J) for these (I,J): (3,520), (5,523), (6,512), (141,525)X(110) = X(I)-cross conjugate of X(J) for these (I,J):
(1,59), (3,250), (6,249), (109,162), (351,111), (512,6), (520,3), (523,54), (526,74)X(110) = crosssum of X(I) and X(J) for these (I,J): (2,148), (512,647), (520,647)
X(110) = crossdifference of any two points on line X(115)X(125)
X(110) = X(I)-Hirst inverse of X(J) for these (I,J): (1,245), (2,125), (3,246), (4,247)
X(110) = X(I)-beth conjugate of X(J) for these (I,J): (21,759), (643,643)