Pedal polygons (Q2871650)

Consider a polygon \(A_1\cdots A_n\) and an arbitrary point \(P\). We denote by \(H_i\) the foor of the perpendicular from \(P\) to the side \(A_iA_{i+1}\) (taking \(A_{n+1}=A_1\)). Then, the polygon (when it exists) \(H_1\cdots H_n\) is called the pedal polygon of \(P\) with respect to the original polygon.NEWLINENEWLINESome interesting results regarding pedal triangles and quadrilaterals are proved. In addition some results are presented for general pedal polygons. In particular, it is proved that if the original polygon is not a parallelogram, then there is exactly one point \(P\) such that the points \(H_i\) are collinear.