## X(98) (TARRY 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           sec(A + ω) : sec(B + ω) : sec(C + ω)
= f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = bc/(b4 + c4 - a2b2 - a2c2)

Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = 1/(b4 + c4 - a2b2 - a2c2)

X(98) = circumcircle-antipode of X(99)
X(98) = the point of intersection, other than A, B, and C, of the circumcircle and Kiepert hyperbola.
X(98) = Ψ(X(101), X(100)

J. W. Clawson, "Points on the circumcircle," American Mathematical Monthly 32 (1925) 169-174.

X(98) lies on these lines:
2,110    3,76    4,32    5,83    6,262    10,101    13,1080    14,383    20,148    22,925    23,94    25,107    30,671    100,228    109,171    186,935    275,427    376,543    381,598    385,511    468,685    523,842    620,631    804,878

X(98) is the {X(2),X(147)}-harmonic conjugate of X(114). For a list of harmonic conjugates, click More at the top of this page.

X(98) = midpoint between X(20) and X(148)
X(98) = reflection of X(I) in X(J) for these (I,J): (4,115), (99,3), (147,114), (1513,230)
X(98) = isogonal conjugate of X(511)
X(98) = isotomic conjugate of X(325)
X(98) = complement of X(147)
X(98) = anticomplement of X(114)
X(98) = X(290)-Ceva conjugate of X(287)
X(98) = cevapoint of X(I) and X(J) for these (I,J): (2,385), (6,237)
X(98) = X(I)-cross conjugate of X(J) for these (I,J): (230,2), (237,6), (248,287), (446,511)
X(98) = crosssum of X(385) and X(401)
X(98) = X(2)-Hirst inverse of X(287)

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