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 a(b4 + c4 - a4) : b(c4 + a4 - b4) : c(a4 + b4 - c4)
Barycentrics a2(b4 + c4 - a4) : b2(c4 + a4 - b4) : c2(a4 + b4 - c4)
Barycentrics sin 2A - tan ω : sin 2B - tan ω : sin 2C - tan ω (M. Iliev, 5/13/07)X(22) is the perspector of the circummedial triangle and the tangential triangle; also X(22) = X(55)-of-the-tangential-triangle if ABC is acute. See the note just before X(1601) for a generalization.
X(22) lies on these lines:
2,3 6,251 32,1194 35,612 36,614 51,182 56,977 69,159 76,1799 98,925 99,305 100,197 110,154 155,1614 157,183 160,325 161,343 184,511 187,1196 232,577 264,1629 347,1617 675,1305 991,1790 1184,1627 1294,1302 1486,1621 1602,1626X(22) is the {X(3),X(25)}-harmonic conjugate of X(2).
X(22) = reflection of X(378) in X(3)
X(22) = isogonal conjugate of X(66)
X(22) = inverse-in-circumcircle of X(858)
X(22) = anticomplement of X(427)
X(22) = X(76)-Ceva conjugate of X(6)
X(22) = cevapoint of X(3) and X(159)
X(22) = crosspoint of X(99) and X(250)
X(22) = crosssum of X(125) and X(512)
X(22) = crossdifference of any two points on line X(647)X(826)
X(22) = X(I)-beth conjugate of X(J) for these (I,J): (643,345), (833,22)