## X(1991) (2ND VAN LAMOEN PERPENDICULAR BISECTORS POINT)

 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            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 inwardly 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(1991). See X(591) for the 1st Van Lamoen perpendicular bisectors point, constructed from outwardly drawn squares.

X(1991) lies on these lines: 2,6    371,754    487,3070    638,1151

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