2012 Fermat Problem 24

In equilateral triangle PQR, S is the midpoint of PR, T is on PQ so that PT = 1 and TQ = 3. Many circles can be drawn inside quadrilateral QRST so that no part extends outside of QRST. The radius of the largest such circle is closest to

\textbf{(A)}\ 1.00\quad \textbf{(B)}\ 1.10\quad \textbf{(C)}\ 1.15\quad \textbf{(D)}\ 1.05\quad \textbf{(E)}\ 1.37

If there are no answer choices shown, enter a numerical answer.

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