Question 142
Triangle $ABC$ has $\angle A = 90^{\circ}$, side $BC = 25$, $AB \gt AC$, and area $150$. Circle $\omega$ is inscribed in $ABC$, with $M$ its point of tangency on $AC$. Line $BM$ meets $\omega$ a second time at point $L$. Find the length of segment $BL$.