X(22) (EXETER POINT)

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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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.

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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           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    1602,1626

X(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)

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