B1 Given a triangle $A B C, X, Y$ are points on side $A B$, with $X$ closer to $A$ than $Y$, and $Z$ is a point on side $A C$ such that $X Z$ is parallel to $Y C$ and $Y Z$ is parallel to $B C$. Suppose $A X=16$ and $X Y=12$. Determine the length of $Y B$.
Solution
Triangles $A X Z$ and $A Y C$ are similar, so $A Z: A X=Z C: X Y$ and so $A Z / Z C=4 / 3$. Also, triangles $A Y Z$ and $A B C$ are similar, so $A Z: Z C=28: Y B$. Combining the two results gives $4 / 3=\frac{28}{Y B}$ so $Y B=21$.