NL-NWO 1973 Problem 1

Given is a triangle $ABC$ , $\angle C = 60^o$ , $R$ the midpoint of side $AB$ . There exist a point $P$ on the line $BC$ and a point $Q$ on the line $AC$ such that the perimeter of the triangle $PQR$ is minimal. a) Prove that and also indicate how the points $P$ and $Q$ can be constructed. b) If $AB = c$ , $AC = b$ , $BC = a$ , then prove that the perimeter of the triangle $PQR$ equals $\frac12\sqrt{3c^2+6ab}$ .