## X(373) (CENTROID OF THE PEDAL TRIANGLE OF THE CENTROID)

 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           f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 2bc + ac cos C + ab cos B
= g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = a(b4 + c4 - a2b2 - a2c2 - 6b2c2)

Barycentrics    h(a,b,c) : h(b,c,a) : h(c,a,b), where h(a,b,c) = 2abc + ca2cos C + ba2cos B

X(373) lies on these lines: 2,51    5,113    110,575    181,748    216,852    354,375

X(373) = crossdifference of any two points on line X(352)X(1499)

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