## X(143) (NINE-POINT CENTER OF ORTHIC TRIANGLE)

 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           f(A,B,C) : f(B,C,A) : f(C,A,B), where
f(A,B,C) = (sec A)[cos(2C - 2A) + cos(2A - 2B)]

Trilinears           g(A,B,C) : g(B,C,A) : g(C,A,B), where
g(A,B,C) = [1 - 2 cos(2A)]cos(B - C)]

Trilinears           h(A,B,C) : h(B,C,A) : h(C,A,B), where
h(A,B,C) = sec A cos(3A) cos(B - C) (Manol Iliev, 4/01/07)

Barycentrics    k(A,B,C) : k(B,C,A) : k(C,A,B), where k(A,B,C) = (tan A)[cos(2C - 2A) + cos(2A - 2B)]

X(143) = X(5)-of-orthic triangle

X(143) lies on these lines: 4,94    5,51    6,26    25,156    30,389    110,195    140,511    324,565

X(143) is the {X(51),X(52)}-harmonic conjugate of X(5).

X(143) = midpoint of X(5) and X(52)
X(143) = isogonal conjugate of X(252)
X(143) = X(137)-cross conjugate of X(1510)

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