## X(1362) (BRISSE TRANSFORM OF X(105))

 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) is as above X(1354), using X = X(105)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(1362) lies on the incircle and these lines:
7,1002    11,118    12,116    43,57    55,103    56,101    59,840    65,1358    105,651    150,388    152,497    928,1361

X(1362) = anticomplement of X(3041)
X(1362) = X(I)-Ceva conjugate of X(J) for these (I,J): (7,241), (651,665)
X(1362) = crosspoint of X(7) and X(241)
X(1362) = crosssum of X(I) and X(J) for (I,J) = (11,885), (55,294)
X(1362) = crossdifference of any two points on line X(294)X(885)
X(1362) = X(672)-Hirst inverse of X(1458)

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