X(2077) (INVERSE-IN-CIRCUMCIRCLE OF X(40))

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
Press the keys “+” and “−” to zoom in or zoom out the visualization window and use the arrow keys to translate it.

You can also construct all centers related with this one (as described in ETC) using the “Run Macro Tool”. To do this, click on the icon , select the center name from the list and, then, click on the vertices A, B and C successively.

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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) = r + 2(r - R) cos A
= g(A,B,C) : g(B,C,A) : g(C,A,B),
where g(A,B,C) = cos 2A + cos B + cos C + (2 cos B + 2 cos C - 3) cos A

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

X(2077) lies on these lines:
1,3    24,1753    30,119    78,1158    84,1259    100,515    102,901    104,519    122,856    376,535    386,601    404,946    516,1519    912,1768    953,1293    972,1308    1012,1376    1593,1878    1618,1818

X(2077) = reflection of X(36) in X(3)
X(2077) = inverse-in-circumcircle of X(40)

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