The Grunert point of pentagons (Q2785018)

The author proves an extension of the following nice result of \textit{J. A. Grunert} [J. reine angew. Math. 4, 396 (1829), 5, 316-317 (1830)], where \(L(A,B)\) denotes the line through the points \(A, B\) in the plane: Given a planar pentagon \(P=ABCDE\), let us denote \(A^*=L(B,C)\cap L(D,E)\), \(B^*=L(C,D)\cap L(E,A),\dots ,\) and let \(A^*A\) be the midpoint of \(A^*\) and \(A\), and \(BE\) the midpoint of \(B\) and \(E\), etc. Then the five lines \(L(A^*A, BE), L(B^*B, AC)\), etc.\ are concurrent. NEWLINENEWLINENEWLINEIn addition to some comments on his result, the author gives some historical information.