## X(396) (MIDPOINT OF X(13) AND X(15))

 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) = cos(B - C) + 2 cos(A - π/3)
Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,B,A)

X(396) lies on these lines:
2,6    3,397    5,14    13,15    16,549    39,619    53,473    62,140    115,531    187,530    203,495    216,466    465,577    532,618    533,623

X(396) is the {X(2),X(6)}-harmonic conjugate of X(395).

X(396) = midpoint of X(I) and X(J) for these (I,J): (13,15), (299,385)
X(396) = reflection of X(395) in X(230)
X(396) = isogonal conjugate of X(2981)
X(396) = anticomplement of X(298)
X(396) = crosspoint of X(2) and X(13)
X(396) = crosssum of X(6) and X(15)
X(396) = crossdifference of any two points on line X(16)X(512)

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