MathNet 2015-part-01 — 191 problems (EN–VI) Question 97

Let $AM$ be the median of the triangle $ABC$, $B_1$ be the foot of the perpendicular $BB_1$ from $B$ onto the bisector of the angle $BMA$, $C_1$ be the foot of the perpendicular $CC_1$ from $C$ onto the bisector of the angle $AMC$. The ray $MA$ intersects the segment $B_1C_1$ at a point $A_1$.
Find the value of the ratio $B_1A_1/A_1C_1$.