Peaucellier-Lipkin linkage

This linkage converts motion along a circle to motion along a straight line. The two GREEN lines are of equal length and fixed at their common end point. The four BLUE lines are of equal length forming a rhombus. Two opposite vertices of the rhombus are connected to the ends of the GREEN lines. Drag the GOLD dot along the circle. Prove that the BLUE dot moves along a straight line.