## X(656) (CROSSDIFFERENCE OF X(1) AND X(19))

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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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            tan B - tan C : tan C - tan A : tan A - tan B
Barycentrics    sin A (tan B - tan C) : sin B (tan C - tan A) : sin C (tan A - tan B)

X(656) lies on these lines: 44,513    240,522    521,810    662,1101    667,832

X(656) = reflection of X(I) in X(J) for these (I,J): (1459,905)
X(656) = isogonal conjugate of X(162)
X(656) = isotomic conjugate of X(811)
X(656) = X(I)-Ceva conjugate of X(J) for these (I,J): (162,1), (163,38)
X(656) = X(125)-cross conjugate of X(201)
X(656) = crosspoint of X(I) and X(J) for these (I,J): (1,162), (521,522)
X(656) = crosssum of X(I) and X(J) for these (I,J): (1,656), (31,661), (108,109), (513,1104), (663,1195)
X(656) = crossdifference of any two points on line X(1)X(19)

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