4. Let $O$ be the center of the inscribed circle of triangle $\triangle A B C$ and $D$ be the point on $A C$ with $O D \perp A C$. If $A B=10 A C=9 B C=11$, find $C D$.
(A) 4
(B) 4.5
(C) 5
(D) 5.5
(E) 6
4. Answer: (C)
$A C$ is tangent to the circle at $D$, by constructing $E$ and $F$ as shown, we have $C D=C F, A D=A E$ and $B E=B F$. Solving for the unknowns give $C D=5$.