## X(650) (CROSSDIFFERENCE OF X(1) AND X(3))

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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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.

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This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears            cos B - cos C : cos C - cos A : cos A - cos B
= (b - c)(b + c - a) : (c - a)(c + a - b) : (a - b)(a + b - c)
Barycentrics    sin A (cos B - cos C) : sin B (cos C - cos A) : sin C (cos A - cos B)
= a(b - c)(b + c - a) : b(c - a)(c + a - b) : c(a - b)(a + b - c)

X(650) lies on these lines:
2,693    44,513    55,884    100,919    230,231    241,514    521,1021    663,861

X(650) = midpoint of X(649) and X(661)
X(650) = isogonal conjugate of X(651)
X(650) = complement of X(693)
X(650) = X(I)-Ceva conjugate of X(J) for these (I,J): (2,11), (100,55), (101,37), (108,33)
X(650) = crosspoint of X(I) and X(J) for these (I,J): (2,100), (57,108), (101,284), (514,522)

X(650) = crosssum of X(I) and X(J) for these (I,J): (1,650), (6,513), (9,521), (73,652), (101,109), (222,905), (226,514), (525,1211), (649,1201), (663,1200), (665,1362)

X(650) = crossdifference of any two points on line X(1)X(3)
X(650) = orthojoin of X(1521)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.