## X(56) (EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE))

 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           a/(b + c - a) : b/(c + a - b) : c/(a + b - c)
= 1 - cos A : 1 - cos B : 1 - cos C
= sin2(A/2) : sin2(B/2) : sin2(C/2)

Barycentrics    a2/(b + c - a) : b2/(c + a - b) : c2/(a + b - c)

The perspector of the tangential triangle and the reflection of the intangents triangle in X(1).

X(56) is the {X(1),X(3)}-harmonic conjugate of X(55).

X(56) = midpoint of X(1) and X(46)
X(56) = reflection of X(I) in X(J) for these (I,J): (1479,496)
X(56) = isogonal conjugate of X(8)
X(56) = anticomplement of X(1329)
X(56) = X(I)-Ceva conjugate of X(J) for these (I,J): (1,221), (7,222), (28,34), (57,6), (59,109), (108,513)
X(56) = X(31)-cross conjugate of X(6)
X(56) = crosspoint of X(I) and X(J) for these (I,J): (1,84), (7,278), (28,58), (57,269), (59,109)

X(56) = crosssum of X(I) and X(J) for these (I,J): (1,40), (2,144), (6,197), (9,200), (10,72), (11,522), (55,219), (175,176), (519,1145)

X(56) = crossdifference of any two points on line X(522)X(650)
X(56) = X(I)-Hirst inverse of X(J) for these (I,J): (6,1458), (34,1430), (57,1429), (604,1428), (1416,1438)
X(56) = X(266)-aleph conjugate of X(1050)
X(56) = X(I)-beth conjugate of X(J) for these (I,J):
(1,1), (21,3), (56,1106), (58,56), and (P,57) for all P on the circumcircle

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