## X(127) (X(112)-OF-MEDIAL-TRIANGLE)

 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) = bc(sin 2B - sin 2C)[(b2 - c2)sin 2A - b2sin 2B + c2sin 2C]

Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where
g(a,b,c) = (sin 2B - sin 2C)[(b2 - c2)sin 2A - b2sin 2B + c2sin 2C]

X(127) lies on the nine-point circle
X(127) = X(112)-of-medial triangle.

X(127) lies on these lines: 2,112    3,114    5,132    113,141    115,338    133,381    125,140

X(127) = reflection of X(132) in X(5)
X(127) = anticomplementary conjugate of X(525)
X(127) = X(4)-Ceva conjugate of X(525)

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