## X(351) (CENTER OF THE PARRY CIRCLE)

 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) = a(b2 - c2)(b2 + c2 - 2a2)
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = a2(b2 - c2)(b2 + c2 - 2a2)

X(351) is the center of the Parry circle introduced in TCCT (Art. 8.13) as the circle that passes through X(I) for I = 2, 15, 16, 23, 110, 111, 352, 353.

X(351) lies on these lines: 2,804    110,526    184,686    187,237    694,881    865,888
X(351) = isogonal conjugate of X(892)
X(351) = crosspoint of X(110) and X(111)
X(351) = crosssum of X(I) and X(J) for these (I,J): (2,690), (523,524), (850,1236)
X(351) = crossdifference of any two points on line X(2)X(99)

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