3. In $\triangle A B C$, $D$ is a point on side $B C$. It is known that $A B=13, A D=12, A C=15, B D=5$, find $D C$.
3. By Stewart's Theorem, we have $A D^{2}=A B^{2} \cdot \frac{C D}{B C}+A C^{2} \cdot \frac{B D}{B C}-B D \cdot D C$. Let $D C=x$, then $B C=5+x$, then $12^{2}=$ $13^{2} \cdot \frac{x}{5+x}+15^{2} \cdot \frac{5}{5+x}-5 x$, solving for $x$ yields $x_{1}=9\left(\right.$ discard $\left.x_{2}=-9\right)$.