## X(32) (3RD POWER POINT)

 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           a3 : b3 : c3
= sin(A - ω) : sin(B - ω) : sin(C - ω)
= sin A + sin(A - 2ω) : sin B + sin(B - 2ω) : sin C + sin(C - 2ω)
= cos A - cos(A - 2ω) : cos B - cos(B - 2ω) : cos C - cos(C - 2ω) (cf., X(39))

Barycentrics    a4 : b4 : c4

X(32) lies on these lines:
1,172    2,83    3,6    4,98    5,230    9,987    21,981    24,232    31,41    56,1015    75,746    76,384    81,980    99,194    100,713    101,595    110,729    163,849    184,211    218,906    512,878    538,1003    561,724    590,640    604,1106    615,639    731,825    733,827    910,1104    993,1107

X(32) is the {X(3),X(6)}-harmonic conjugate of X(39).

X(32) = midpoint of X(371) and X(372)
X(32) = reflection of X(315) in X(626)
X(32) = isogonal conjugate of X(76)
X(32) = isotomic conjugate of X(1502)
X(32) = inverse-in-circumcircle of X(1691)
X(32) = inverse-in-Brocard-circle of X(39)
X(32) = inverse-in-1st-Lemoine-circle of X(1692)
X(32) = complement of X(315)
X(32) = anticomplement of X(626)
X(32) = X(I)-Ceva conjugate of X(J) for these (I,J): (2,206), (6,184), (112,512), (251,6)
X(32) = crosspoint of X(I) and X(J) for these (I,J): (2,66), (6,25)

X(32) = crosssum of X(I) and X(J) for these (I,J): (2,69), (6,22), (75,312), (115,826), (311,343), (313,321), (338,850), (339,525), (349,1231), (693,1086), (1229,1233), (1230,1269)

X(32) = crossdifference of any two points on line X(325)X(523)
X(32) = X(184)-Hirst inverse of X(237)
X(32) = X(I)-beth conjugate of X(J) for these (I,J): (41,41), (163,56), (919,32)
X(32) = external center of similitude of circumcircle and Moses circle

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