## X(1692) (RADICAL TRACE OF CIRCUMCIRCLE AND 2ND LEMOINE CIRCLE)

 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           f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = 2 sin(A - 2ω) + sin(A + 2ω) - sin A
Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

X(1692) lies on these lines: 3,6    51,1501    114,230    115,1503    184,1196    698,1569    1015,1428    1627,1994

X(1692) = midpoint of X(I) and X(J) for these (I,J): (6,1691), (187,1570)
X(1692) = reflection of X(I) in X(J) for these (I,J): (39,2024), (187,1570), (1570,6)
X(1692) = inverse-in-circumcircle of X(3053)
X(1692) = inverse-in-1st-Lemoine-circle of X(32)
X(1692) = inverse-in-2nd-Lemoine-circle of X(1351)
X(1692) = crosspoint of X(I) and X(J) for these (I,J): (6,1976), (230,460)
X(1692) = crosssum of X(2) and X(325)

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