## X(1015) (EXSIMILICENTER OF MOSES CIRCLE AND 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            a(b - c)2 : b(c - a)2 : c(a - b)2
Barycentrics    a2(b - c)2 : b2(c - a)2 : c2(a - b)2

The circle having center X(39) and radius 2R sin2ω, where R denotes the circumradius of triangle ABC, is here introduced as the Moses circle. It is tangent to the nine-point circle at X(115), and its internal and external centers of similitude with the incircle are X(1500) and X(1015), respectively. (Peter J. C. Moses, 5/29/03)

X(1015) lies on these lines:
1,39    2,668    6,101    11,115    32,56    36,187    37,537    55,574    76,330    214,1100    216,1060    244,665    350,538    812,1086

X(1015) = midpoint of X(1) and X(291)
X(1015) = isogonal conjugate of X(1016)
X(1015) = complement of X(668)
X(1015) = crosspoint of X(2) and X(513)
X(1015) = crosssum of X(I) and X(J) for these (I,J): (1,1018), (2,190), (6,100), (8,644), (101,595), (345,1332)
X(1015) = crossdifference of any two points on line X(100)X(190)

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