X(343) (ISOTOMIC CONJUGATE OF X(275))

 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           cot A cos(B - C) : cot B cos(C - A) : cot C cos(A - B)
Barycentrics    cos A cos(B - C) : cos B cos(C - A) : cos C cos(A - B)

X(343) lies on these lines:
2,6    3,68    5,51    22,161    53,311    76,297    140,569    315,458    427,511    470,634    471,633    472,621    473,622

X(343) = isotomic conjugate of X(275)
X(343) = complement of X(1993)
X(343) = X(I)-Ceva conjugate of X(J) for these (I,J): (76,311), (311,5)
X(343) = X(216)-cross conjugate of X(5)
X(343) = crosspoint of X(69) and X(76)
X(343) = crosssum of X(I) and X(J) for these (I,J): (6,571), (25,32)

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