Construction

1. Take segment MN with length equal to P
2. Draw the angle MNA equal to beta/2
3. Draw the angle NMA equal to gamma/2
   Both sides NA and MA meet at point A which is the first vertex of the triangle requested
4. Draw the perpendicular bisector EB of segment NA.
   (Point E is midpoint of the segment AN)
   Segment EB crosses the segment MN at point B which is the second vertex of the triangle requested.
5. Draw the perpendicular bisector DC of segment MA.
   (Point D is midpoint of the segment AM)
   Segment DC crosses the segment MN at point C which is the third vertex of the triangle requested.