Proof of Laguerre's theorem and its extensions by the method for polar coordinates (Q1358964)

The paper presents a new proof of the following theorem (of Laguerre): Given 5 points \(A_1, A_2, A_3, A_4\) and \(P\) on a circle, it is possible to determine the Wallace (or Simpson)-lines \(s_i\) of the triangles \(A_j, A_k, A_l\) for all permutations of \((i,j,k,l)\). \(D_i\) shall denote the pedal points of \(s_i\) with respect to \(P\). Then the author is able to proof, that the 4 points \(D_i\) \((i= 1,2,3,4)\) lie on one straight line. In addition, extensions to more points on a circle are discussed in the paper.