## X(1656) (INTERSECTION OF EULER LINE AND LINE X(17)X(18))

 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           f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = 3 cos A + 4 cos B cos C
Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

X(1656) lies on these lines:
2,3    6,17    10,1482    11,498    12,499    49,569    51,1216    125,399    141,1351    302,634    303,633    355,1125    373,568    485,615    486,590    517,1698    567,1147    576,599

X(1656) = midpoint of X(5) and X(632)
X(1656) = reflection of X(I) in X(J) for these (I,J): (3,631), (631,632)
X(1656) = inverse-in-orthocentroidal-circle of X(140)
X(1656) = complement of X(631)
X(1656) = anticomplement of X(632)

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