## X(1659) (YIU-PAASCHE 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           f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = 1/(1 + sin A + cos A)
Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

For a discussion of this point, see

Paul Yiu, Introduction to the Geometry of the Triangle, 2002, Article 3.5.4 Exercise 4d.
(The preceding Exercise 4c presents the Paasche point, X(1123),) (Contributed by Darij Grinberg, 8/24/03)

X(1659) lies on these lines: 1,4    2,176    57,482    75,491    92,1585    553,1373

X(1659) = isogonal conjugate of X(2066)
X(1659) = X(482)-cross conjugate of X(7)
X(1659) = crosssum of X(48) and X(605)

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