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So I was going to upvote your question as I am curious of the same thing, but since my karma isn't high enough I'll just have to comment.

What you have so far looks great, the center you found is the same answer we got in class working it out on the board. So take this vote of confidence as an answer to the first part of your question, unfortunately I am stumped as to how to continue.

Hopefully someone can add a more complete answer to the question but I'll be sure to post again if I happen to figure it out.