## X(589) (2ND KENMOTU-VAN LAMOEN POINT)

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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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/(a2 - 4*area(ABC))
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

X(589) is the perspector of triangles ABC and A'B'C', where A' is the circumcenter of X(372) and the points where the squares in the Kenmotu configuration with center X(372) meet sideline BC, and B' and C' are defined cyclically. See the reference at X(588).

X(589) lies on this line: 39,588

X(589) = isogonal conjugate of X(615)
X(589) = cevapoint of X(6) and X(372)
X(589) = X(1994)-cross conjugate of X(588)

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