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(A + π/6) : csc(B + π/6) : csc(C + π/6)
= sec(A - π/3) : sec(B - π/3) : sec(C - π/3)Barycentrics a csc(A + π/6) : b csc(B + π/6) : c csc(C + π/6)
Let X,Y,Z be the centers of the equilateral triangles in the construction of X(13). The lines AX, BY, CZ concur in X(17).
John Rigby, "Napoleon revisited," Journal of Geometry, 33 (1988) 126-146.
X(17) lies on these lines:
2,62 3,13 4,15 5,14 6,18 12,203 16,140 76,303 83,624 202,499 275,471 299,635 623,633X(17) is the {X(231),X(1209)}-harmonic conjugate of X(18).
X(17) = reflection of X(627) in X(629)
X(17) = isogonal conjugate of X(61)
X(17) = isotomic conjugate of X(302)
X(17) = complement of X(627)
X(17) = anticomplement of X(629)
X(17) = X(I)-cross conjugate of X(J) for these (I,J): (16,14), (140,18), (397,4)