Problem

Source: V.A. Yasinsky Geometry Olympiad 2019 X-XI advanced p2 [Ukraine]

Tags: geometry, perimeter, 3D geometry, pyramid, rectangle



The base of the quadrilateral pyramid $SABCD$ lies the $ABCD$ rectangle with the sides $AB = 1$ and $AD = 10$. The edge $SA$ of the pyramid is perpendicular to the base, $SA = 4$. On the edge of $AD$, find a point $M$ such that the perimeter of the triangle of $SMC$ was minimal.