## X(291) (2ND SHARYGIN POINT)

 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           1/(a2 - bc) : 1/(b2 - ca) : 1/(c2 - ab)
Barycentrics    a/(a2 - bc) : b/(b2 - ca) : c/(c2 - ab)

See the description at X(1281). The lines AD', BE', CF' defined there concur in X(256).

X(291) lies on these lines: 1,39    2,38    6,985    8,330    10,274    42,81    43,57    88,660    105,238    256,894    337,986    350,726    659,897    876,891

X(291) = reflection of X(I) in X(J) for these (I,J): (1,1015), (668,10)
X(291) = isogonal conjugate of X(238)
X(291) = isotomic conjugate of X(350)
X(291) = X(I)-cross conjugate of X(J) for these (I,J): (239,256), (518,1)
X(291) = X(I)-Hirst inverse of X(J) for these (I,J): (1,292), (2,335)

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