The Euler line revisited
The authors show: If there is a point \(P\) and a triangle \(ABC\) in the plane such that \({PA\over BC}={PB\over AC}={PC\over AB}\), then \(P\) lies on the Euler line. The existence and the number (up to 2) of such points \(P\) depends on the angles of the triangle.
scientific article; zbMATH DE number 513264