Equilibrium equations for circular lamp base with angled arm

[dealdoe22]

Just joined PF and my mind is completely shutting down on me.

I need to design the base of a halogen desk lamp and am having a problem getting started. My biggest problem is finding the correct equation to use to begin calculating the numbers. It is a three dimensional problem. Can someone please help me with this.



I have attached a pdf file of the diagrams and known information. The basics are that the base needs to be circular and angles α and β are measured horizontally regardless of their position.

 

[dealdoe22]

Sorry. I don't think I attached the pdf on the first try.

 

[nvn]

dealdoe22: You must list relevant equations yourself, and show your work. And then someone might check your math. We are not allowed to give you the relevant equations for your homework.