## X(591) (1ST VAN LAMOEN PERPENDICULAR BISECTORS POINT)

 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) = bc[b2 + c2 - 2a2 + 4*area(ABC)]
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

Erect squares outwardly on the sides of triangle ABC. Two edges emanate from A; let P and Q be their endpoints. Let a' be the perpendicular bisector of PQ, and define b' and c' cyclically. Then a', b', c' concur in X(591). See also X(1991). (Floor van Lamoen, 1/4/01, Hyacinthos #2123)

X(591) lies on these lines: 2,6    372,754    488,3071    637,1152

X(591) = reflection of X(1991) in X(2)

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