Problem

Source: V.A. Yasinsky Geometry Olympiad 2018 X-XI p4, advanced p2 [Ukraine]

Tags: geometry, circumcircle, circumradius, minimum



Let $ABC$ be an acute triangle. A line, parallel to $BC$, intersects sides $AB$ and $AC$ at points $M$ and $P$, respectively. At which placement of points $M$ and $P$, is the radius of the circumcircle of the triangle $BMP$ is the smallest?