## X(497) (CROSSPOINT OF GERGONNE POINT AND NAGEL POINT)

 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           1 - cos B cos C : 1 - cos C cos A : 1 - cos A cos B
Barycentrics    (sin A)(1 - cos B cos C) : (sin B)(1 - cos C cos A) : (sin C)(1 - cos A cos B)

X(497) is the harmonic conjugate of X(388) with respect to X(1) and X(4)

X(497) lies on these lines:
1,4    2,11    3,496    7,354    8,210    20,56    29,1036    30,999    35,499    36,376    57,516    65,938    69,350    80,1000    212,238    329,518    381,495    452,958    614,1040    1057,1065

X(497) = isogonal conjugate of X(1037)
X(497) = anticomplement of X(1376)
X(497) = crosspoint of X(I) and X(J) for these (I,J): (7,8), (29,314)
X(497) = crosssum of X(I) and X(J) for these (I,J): (55,56), (73,1402)
X(497) = crossdifference of any two points on line X(652)X(665)

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