## X(111) (PARRY 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           a/(2a2 - b2 - c2) : b/(2b2 - c2 - a2) : c/(2c2 - a2 - b2)
Barycentrics    a2/(2a2 - b2 - c2) : b2/(2b2 - c2 - a2) : c2/(2c2 - a2 - b2)

X(111) = Λ(X(2), X(6))

X(111) lies on these lines:
2,99    6,110    23,187    25,112    37,100    42,101    107,393    182,353    230,476    251,827    308,689    352,511    385,892    468,935    512,843    647,842    694,805    931,941

X(111) = reflection of X(1296) in X(3)
X(111) = isogonal conjugate of X(524)
X(111) = inverse-in-Brocard-circle of X(353)
X(111) = anticomplement of X(126)
X(111) = cevapoint of X(6) and X(187)
X(111) = X(I)-cross conjugate of X(J) for these (I,J): (23,251), (187,6), (351,110)
X(111) = crossdifference of any two points on line X(351)X(690)

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