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Good Afternoon,

I have spent a couple of hours trying to solve this problem, but it appears that I have not gotten anywhere.

Let $R$,$P$,$Q$ be points such that $\angle RQP=75^\circ$. Also we are given that $RQ=\sqrt{2}$ and $PQ=\sqrt{3}$. A lens is a region bounded by two circular arcs meeting at the endpoints. Let $m$ be the area of the largest lens that does not intersect lines $QR$ and $QP$, with endpoints at $R$ and $P$. How would we find $m$?

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    This is from the **ongoing** [USAMTS competition (problem 4)](http://www.usamts.org/Tests/Problems_23_2.pdf). Of course, Alan, I'm sure you are aware that it would against [the rules of the competition](http://www.usamts.org/Rules/U_RulesComplete.php) to submit this as an answer - so you're just asking out of curiosity. Right?2011-11-05

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