X(2070) (INVERSE-IN-CIRCUMCIRCLE OF X(5))

 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) = (J2 - 2) cos A + 4 cos B cos C, where J is as at X(1113)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(2070) lies on these lines:
2,3    49,52    51,567    54,143    98,1287    110,1154    184,568    187,2079    231,1989    399,1495    476,1141    500,501    827,842

X(2070) = midpoint of X(23) and X(186)
X(2070) = reflection of X(I) in X(J) for these (I,J): (3,186), (2072,468)
X(2070) = inverse-in-circumcircle of X(5)
X(2070) = X(94)-Ceva conjugate of X(6)
X(2070) = crosspoint of X(I) and X(J) for these (I,J): (250,476), (1141,1166)
X(2070) = crosssum of X(I) and X(J) for these (I,J): (125,526), (1154,1209)

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