## X(381) (MIDPOINT OF X(2) AND X(4))

 Interactive Applet

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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           2 cos(B - C) - cos A : 2 cos(C - A) - cos B : 2 cos(A - B) - cos C
= cos A + 4 cos B cos C : cos B + 4 cos C cos A : cos C + 4 cos A cos B

Barycentrics    a(cos A + 4 cos B cos C) : b(cos B + 4 cos C cos A) : c(cos C + 4 cos A cos B)

X(381) = center of the orthocentroidal circle

X(381) lies on these lines:
2,3    6,13    11,999    49,578    51,568    54,156    98,598    114,543    118,544    119,528    125,541    127,133    155,195    183,316    184,567    210,517    262,671    264,339    298,622    299,621    302,616    303,617    355,519    388,496    495,497    511,599    515,551

X(381) is the {X(4),X(5)}-harmonic conjugate of X(3) and also the {X(13),X(14)}-harmonic conjugate of X(6).

X(381) = midpoint of X(2) and X(4)
X(381) = reflection of X(I) in X(J) for these (I,J): (2,5), (3,2), (376,549), (549,547), (568,51)
X(381) = complement of X(376)
X(381) = anticomplement of X(549)
X(381) = crossdifference of any two points on line X(526)X(647)

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