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 sec A cos 2A : sec B cos 2B : sec C cos 2C
= sec A - 2 cos A : sec B - 2 cos B : sec C - 2 cos CBarycentrics tan A cos 2A : tan B cos 2B : tan C cos 2C
= tan A - sin 2A : tan A - sin 2B : tan C - sin 2C
Constructed as indicated by the name; also X(24) = X(56)-of-the-tangential triangle if ABC is acute.
X(24) lies on these lines:
1,1061 2,3 6,54 32,232 33,35 34,36 49,568 51,578 52,1147 56,1870 64,74 96,847 98,1289 107,1093 108,915 110,155 154,1181 182,1843 183,1235 184,389 185,1495 242,1602 254,393 264,1078 511,1092 573,1474 602,1395 944,1610 1063,1775 1112,1511 1192,1511 1324,1603 1385,1829X(24) is the {X(3),X(4)}-harmonic conjugate of X(378).
X(24) = reflection of X(4) in X(235)
X(24) = isogonal conjugate of X(68)
X(24) = inverse-in-circumcircle of X(403)
X(24) = X(249)-Ceva conjugate of X(112)
X(24) = X(52)-cross conjugate of X(4)
X(24) = crosspoint of X(107) and X(250)
X(24) = crosssum of X(I) and X(J) for these (I,J): (6,161), (125,520), (637,638)
X(24) = X(4)-Hirst inverse of X(421)