3. On the side $B C$ of triangle $A B C$ with obtuse angle $C$, a point $M$ is marked. Point $D$ is chosen such that triangle $B C D$ is acute, and points $A$ and $D$ lie on opposite sides of line $B C$. Circles $\omega_{B}$ and $\omega_{C}$ are circumscribed around triangles $B M D$ and $C M D$ respectively. Side $A B$ intersects circle $\omega_{B}$ again at point $P$, and ray $A C$ intersects circle $\omega_{C}$ again at point $Q$. Segment $P D$ intersects circle $\omega_{C}$ again at point $R$, and ray $Q D$ intersects circle $\omega_{B}$ again at point $S$. Find the ratio of the areas of triangles $A B R$ and $A C S$.