A geometric inequality with applications (Q2830080)

In the paper under review, the author proves an inequality involving the distance from a point in a plane of a triangle to the vertices and the sides of the triangle as well as the circumradius of the triangle and the distance from the point to the circumcenter of the triangle. Furthermore, it is shown that equality holds instead of the inequality if and only if the given point lies on the line joining the circumcenter to the Lhuillier-Lemoine point of the triangle.NEWLINENEWLINEAs a consequence, the author obtains a simpler proof of another inequality which he had proved previously, as well as a proof of an inequality known as the Sondat fundamental inequality.