Question 22
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 $BD \gt 5\sqrt{2}?$
