## X(576) (ORTHOHARMONIC OF X(187))

 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) = sin A + cot D/2 cos A,
cot D/2 = - (a2 + b2 + c2)/(12*area)

Trilinears            g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = 3 sin A - cos A cot ω    (Peter J. C. Moses, 7/20/03)

Trilinears            h(A,B,C) : h(B,C,A) : h(C,A,B), where h(A,B,C) = cos A - 3 sin A tan ω    (Peter J. C. Moses, 8/22/03)

Barycentrics    (sin A)f(A,B,C): (sin B)f(B,C,A) : (sin C)f(C,A,B)

X(576) lies on these lines: 3,6    4,542    5,524    23,184    140,597    262,385

X(576) = reflection of X(I) in X(J) for these (I,J): (3,575), (182,6)
X(576) = inverse-in-Brocard-circle of X(575)
X(576) = inverse-in-2nd-Lemoine-circle of X(1691)

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