Calculus of Variations - Circles with soapy membrane problem

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Calculus of variations is coming to me at a crawl pace. Here is a problem on my agenda that I wanted to get solved, but am not quite sure how to approach. I've been thinking about it for a while now. I figured everybody would appreciate a scanned image instead of a declaration of text, so here is a scanned image.

I'll continue to work the problem for the next several hours or so alongside the others I wanted to complete, but as always, if somebody knows a valid solution using calculus of variations it would sure help a bunch since this specific problem is only study material.

Soap Membrane