## X(316) (DROUSSENT PIVOT)

 Interactive Applet

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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) = bc(b4 + c4 - a4 - b2c2)
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = b4 + c4 - a4 - b2c2

The reflection of X(99) in the polar of X(76).

Lucien Droussent, "Cubiques circulaires anallagmatiques par points réciproques ou isogonaux," Mathesis 62 (1953) 204-215.

X(316) lies on these lines:
2,187    4,69    15,303    16,302    30,99    115,385    148,538    183,381    249,297    265,290    298,530    299,531    376,1007    384,626    512,850    524,671    691,858

X(316) = midpoint of X(621) and X(622) X(316) = reflection of X(I) in X(J) for these (I,J): (15,624), (16,623), (99,325), (385,115), (691,858)
X(316) = isotomic conjugate of X(67)
X(316) = anticomplement of X(187)
X(316) = crosssum of X(39) and X(187)

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