## X(1577) (ISOGONAL CONJUGATE OF X(163))

 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           b2c2(b2 - c2) : c2a2(c2 - a2) : a2b2(a2 - b2)
Barycentrics    bc(b2 - c2) : ca(c2 - a2) : ab(a2 - b2)

X(1577) is the perspector of the excentral triangle and the apices of equilateral triangles constructed inward from the sides, as in the construction of X(14). (Paul Yiu, 2/27/04).

X(1577) lies on these lines:
1,810    115,1111    163,811    240,522    514,661    667,814    784,149    798,812    826,1089

X(1577) = isogonal conjugate of X(163)
X(1577) = isotomic conjugate of X(662)
X(1577) = X(I)-Ceva conjugate of X(J) for these (I,J): (75,1109), (76,1111), (693,523), (799,75), (811,1), (823,92)
X(1577) = cevapoint of X(656) and X(661)
X(1577) = X(I)-cross conjugate of X(J) for these (I,J): (115,1089), (1109,75)
X(1577) = crosspoint of X(I) and X(J) for these (I,J): (75,799), (82,162), (92,823), (662,2167), (811,1969), (1240,1978)
X(1577) = crosssum of X(I) and X(J) for these (I,J): (31,798), (38,656), (48,822), (649,2260), (652,2269), (661,1953), (1923,1924)
X(1577) = crossdifference of any two points on line X(31)X(48)
X(1577) = X(I)-aleph conjugate of X(J) for these (I,J): (648,656), (811,1969)

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