ÖMO 2004 Problem 6

Over the sides of an equilateral triangle with area $1$ are triangles with the opposite angle $60^{\circ}$ to each side drawn outside of the triangle. The new corners are $P$ , $Q$ and $R$ . (and the new triangles $APB$ , $BQC$ and $ARC$ ) 1)What is the highest possible area of the triangle $PQR$ ? 2)What is the highest possible area of the triangle whose vertexes are the midpoints of the inscribed circles of the triangles $APB$ , $BQC$ and $ARC$ ?