## X(122) (X(107)-OF-MEDIAL-TRIANGLE)

 Interactive Applet

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 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) = (b2 - c2)2(cos A - cos B cos C) cot2A

Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b) where g(a,b,c) = a(b2 - c2)2(cos A - cos B cos C) cot2A

X(122) lies on the nine-point circle
X(122) = X(107)-of-medial triangle.

X(122) lies on these lines: 2,107    3,113    5,133    118,440    125,684    138,233

X(122) = reflection of X(133) in X(5)
X(122) = complementary conjugate of X(520)
X(122) = X(I)-Ceva conjugate of X(J) for these (I,J): (4,520), (253,525)
X(122) = crosssum of X(I) and X(J) for these (I,J): (64,1301), (112,154)
X(122) = crosspoint of X(253) and X(525)
X(122) = crossdifference of any two points on line X(112)X(1301)

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