# Problem #945

 945 Triangle $ABC$ is a right triangle with $\angle ACB$ as its right angle, $m\angle ABC = 60^{\circ}$, and $AB = 10$. Let $P$ be randomly chosen inside $\triangle ABC$, and extend $\overline{BP}$ to meet $\overline{AC}$ at $D$. What is the probability that $BD > 5\sqrt{2}$? $\textbf{(A)}\ \frac{2-\sqrt2}{2}\qquad\textbf{(B)}\ \frac{1}{3}\qquad\textbf{(C)}\ \frac{3-\sqrt3}{3}\qquad\textbf{(D)}\ \frac{1}{2}\qquad\textbf{(E)}\ \frac{5-\sqrt5}{5}$ This problem is copyrighted by the American Mathematics Competitions.
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