## SUBJECT 3

Let the collinear points $A, B, C, D$ in this order, such that $5 A B=9 A C-4 A D$ and $B D=18 \mathrm{~cm}$.

a) Find the lengths of the segments $B C$ and $D C$.

b) If $P$ is the midpoint of segment $A D$ and $P \in(B C)$, specify the maximum possible value, a natural number, of the length of segment AD.