## X(495) (JOHNSON MIDPOINT)

 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           2 + cos(B - C) : 2 + cos(C - A) : 2 + cos(A - B)
Barycentrics    (sin A)[2 + cos(B - C)] : (sin B)[2 + cos(C - A)] : (sin C)[2 + cos(A - B)]

X(495) is the midpoint of segments C1-to-P1, C2-to-P2, C3-to-P3 in the Johnson four-circle configuration.

Roger A. Johnson, Advanced Euclidean Geometry, Dover, New York, 1960, page 75.

Peter Yff, "Three concurrent congruent circles 'inscribed' in a triangle," manuscript, 1998; X(495) is the point R on page 5. (See also X(496)-X(499) and X(1478), X(1479).)

X(495) lies on these lines:
1,5    2,956    3,388    4,390    8,442    10,141    30,55    35,550    36,549    56,140    202,395    203,396    226,517    381,497    392,908    429,1068    529,993    612,1060

X(495) = complement of X(956)

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