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 2 cos A + cos(B - C) : 2 cos B + cos(C - A) : 2 cos C + cos(A - B)
= cos A + 2 sin B sin C : cos B + 2 sin C sin A : cos C + 2 sin A sin B
= 3 cos A + 2 cos B cos C : 3 cos B + 2 cos C cos A : 3 cos C + 2 cos A cos B
= f(a,b,c) : f(b,c,a) : f(c,a,b), where
f(a,b,c) = bc[b cos(C - A) + c cos(B - A)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b) where g(a,b,c) = b cos(C - A) + c cos(B - A)
X(140) lies on the Euler line
X(140) = crosspoint of the two Napoleon points
X(140) = X(5)-of-medial triangle
X(140) lies on these lines:
2,3 10,214 11,35 12,36 15,18 16,17 39,230 54,252 55,496 56,495 61,395 62,396 95,340 125,128 141,182 143,511 195,323 298,628 299,627 302,633 303,634 343,569 371,615 372,590 524,575 576,597 601,748 602,750 618,630 619,629X(140) is the {X(2),X(3)}-harmonic conjugate of X(5).
X(140) = midpoint of X(I) and X(J) for these (I,J): (3,5), (141,182)
X(140) = reflection of X(I) in X(J) for these (I,J): (546,5), (547,2), (548,3)
X(140) = inverse-in-orthocentroidal-circle of X(1656)
X(140) = isogonal conjugate of X(1173)
X(140) = complement of X(5)
X(140) = complementary conjugate of X(1209)
X(140) = X(2)-Ceva conjugate of X(233)
X(140) = crosspoint of X(I) and X(J) for these (I,J): (2,95), (17,18)
X(140) = crosssum of X(I) and X(J) for these (I,J): (6,51), (61,62)