The Cevian Simson transformation (Q2878863)

A special plane transformation is introduced in the paper under review. For a given point \(M\) in the plane of the triangle \(ABC\) it is determined the point \(P\) such that the cevians passing through \(M\) are parallel to the Simson lines passing through \(P\). The mapping that sends \(M\) onto \(P\) is called the Cevian Simson transformation (CST). The author studies the properties of the CST. He obtains the CST images of remarkable points, lines, quadrics and cubics connected with the triangle \(ABC\).