## X(1503) (ORTHOPOINT OF X(525))

 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) = bc(b6 + c6 - 2a6 + a4b2 + a4c2 - b4c2 - c4b2)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(1503) lies on these lines:
2,154    3,66    4,6    5,182    11,1428    20,64    22,161    30,511    51,428    67,74    98,230    110,858    125,468    147,325    184,427    221,388    242,1146    265,1177    287,297    376,599    381,597    382,1351    383,395    394,1370    396,1080    546,575    576,1353    611,1478    613,1479    946,1386

X(1503) = isogonal conjugate of X(1297)
X(1503) = complementary conjugate of X(132)
X(1503) = X(I)-Ceva conjugate of X(J) for these (I,J): (4,132), (287,6), (297,230), (685,523)
X(1503) = cevapoint of X(20) and X(147)
X(1503) = crosspoint of X(4) and X(98)
X(1503) = crosssum of X(3) and X(511)
X(1503) = crossdifference of any two points on line X(6)X(520)
X(1503) = X(4)-Hirst inverse of X(1249)

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