Interactive Applet |
You can move the points A, B and C (click on the point and drag it).
Press the keys “+” and “−” to zoom in or zoom out the visualization window and use the arrow keys to translate it.
You can also construct all centers related with this one (as described in ETC) using the “Run Macro Tool”. To do this, click on the icon , select the center name from the list and, then, click on the vertices A, B and C successively.
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 163,811 240,522 514,661 667,814 784,149 798,812 826,1089X(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)