## X(1500) (INSIMILICENTER OF MOSES CIRCLE AND INCIRCLE)

 Interactive Applet

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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 R tan ω sin 2ω, 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(1500) lies on these lines:
1,39    6,595    10,37    11,1508    12,115    32,55    35,172    41,1017    42,213    56,574    76,192    216,1062    346,941    519,1107    612,1196    756,762    1124,1505    1335,1504

X(1500) = isogonal conjugate of X(1509)
X(1500) = X(I)-Ceva conjugate of X(J) for these (I,J): (37,756), (42,872), (1018,512)
X(1500) = X(872)-cross conjugate of X(181)
X(1500) = crosspoint of X(37) and X(42)
X(1500) = crosssum of X(81) and X(86)

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