## X(2447) (2ND INTERSECTION(LINE X(1)X(3), INCIRCLE))

 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) = cos B + cos C - 1 + D,
D = (3 - 2 cos A - 2 cos B - 2 cos C)1/2

Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

Of the two points of intersection, X(2447) is the farther from to X(3).

X(2447) lies on the incircle and these lines: 1,3    2170,2591

X(2447) = reflection of X(2446) in X(1)
X(2447) = X(I)-Ceva conjugate of X(J) for these I,J: 57,2591    1381,513
X(2447) = crosssum of X(1) and X(1382)

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