## X(376) (CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2))

 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           5 cos A - cos(B - C) : 5 cos B - cos(C - A) : 5 cos C - cos(A - B)
= 2 cos A - cos B cos C : 2 cos B - cos C cos A : 2 cos C - cos A cos B
= f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = (csc A)(5 sin 2A - sin 2B - sin 2C)

Barycentrics    g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = 5 sin 2A - sin 2B - sin 2C

X(376) is the reflection of X(2) in X(3).

X(376) lies on these lines:
1,553    2,3    35,388    36,497    40,519    55,1056    56,1058    69,74    98,543    103,544    104,528    110,541    112,577    165,515    316,1007    390,999    476,841    477,691    487,490    488,489    516,551

X(376) is the {X(3),X(20)}-harmonic conjugate of X(4).

X(376) = midpoint of X(2) and X(20)
X(376) = reflection of X(I) in X(J) for these (I,J): (2,3), (4,2), (381,549)
X(376) = anticomplement of X(381)

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