X(132) (X(105)-OF-ORTHIC-TRIANGLE)

 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) = (sec A) u(A,B,C) v(A,B,C),
u(A,B,C) = [sin2(2A) + (sin 2B - sin 2C)2 + (sin 2A)(sin 2A - sin 2B - sin 2C)],
v(A,B,C) = [sin2(2B) + sin2(2C) - (sin 2A sin 2B) - (sin 2A sin 2C)]

Barycentrics    g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A) f(A,B,C)

X(132) lies on the nine-point circle
X(132) = X(105)-of-orthic triangle

X(132) lies on these lines: 2,107    4,32    5,127    25,136    51,125    114,684    137,428    147,648

X(132) = midpoint of X(4) and X(112)
X(132) = reflection of X(127) in X(5)
X(132) = X(I)-Ceva conjugate of X(J) for these (I,J): (2,232), (4,1503)
X(132) = X(4)-line conjugate of X(248)
X(132) = crossdifference of any two points on line X(248)X(684)

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