## X(1570) (MOSES-CIRCLE INVERSE OF X(3))

 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) = a(cot A + cot ω - 4 tan ω)

Trilinears            g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = cos A + (sin A)(cot ω - 4 tan ω)

Trilinears            h(a,b,c) : h(b,c,a) : h(c,a,b), where h(a,b,c) = a(2a4 + 3b4 + 3c4 - 2b2c2 - 3a2b2 - 3a2c2)

Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(1570) = 2nd-Lemoine-circle inverse of X(3)
X(1570) = radical trace of the Brocard and 2nd Lemoine circles

X(1570) lies on these lines: 3,6    193,625

X(1570) = reflection of X(I) in X(J) for these (I,J): (39,2025), (187,1692), (1692,6)
X(1570) = inverse-in-2nd-Lemoine-circle of X(3)
X(1570) = crosssum of X(2) and X(230)

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