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V-Plotter problem (rod suspended by two strings)

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Hi, I'm building a vplotter (pen suspended by two strings of varying length) and I am facing a problem that looked quite simple at first but I'm finding myself struggling with my rusty math skills. Maybe someone could point me in the right direction. So here's the problem:An object, to make it easier, a rod, is suspended at it's ends to a ceiling by two strings.I know the coordinates of points A and D as well as the length of the strings a,c and the distance between B and C (b in the drawing). I need to find the coordinates for B and C when the system is in equilibrium. This is where I am at: Point B lies on the circle around A with the radius a. C lies on the circle around D with the radius c. So, with (x-a)2+(y-b)2=r2 (Circle) I have: (1) (xB - xA)2 + (yB - yA)2 = a2 (2) (xC - xD)2 + (yC - yD)2 = c2 Also, |BC| = b (distance between B and C is given). So: (3) b = sqrt( (xB-xC)2 + (yB-yC)2 ) => b2 = (xB-xC)2 + (yB-yC)2 This is where I'm getting into trouble (or maybe I already am). 4 unknowns, only 3 equations. My system still has a degree of freedom, I suppose the physical equivalent of shifting the rod around on the two circles. I was hoping I'd get another equation by looking at how gravity exerts forces on the rod and those forces split into tangential and perpendicular forces at points B and C. Knowing that the system is in equilibrium, all those forces should add to 0. This is where I am stuck. Any help would be greatly appreciated. Maybe someone can point me in the right direction to move on or point out any mistakes so far. Thanks