2. Given is $\triangle A B C$. A line parallel to $A C$ intersects side $A B$ at point $P$, the median $A A_{1}$ at point $K$, and side $B C$ at point $L$. If $P K=7$ and $K L=5$, determine the length of side $A C$.
2. Let's draw a line through point $K$ that is parallel to $BC$, and denote its intersections with $AB$ and $AC$ as $D$ and $E$. From Thales' theorem, we have $\frac{C A_{1}}{E K}=\frac{A_{1} A}{K A}$ and $\frac{B A_{1}}{D K}=\frac{A_{1} A}{K A}$, i.e., $\frac{C A_{1}}{E K}=\frac{B A_{1}}{D K}$. Given that $B A_{1}=C A_{1}$, it follows that $D K = E K$, i.e., $K$ is the midpoint of segment $DE$. Therefore, $KP$ is the midline of $\triangle ADE$ and thus $A E = 2 K P = 14$. On the other hand, $E K L C$ is a parallelogram, so $E C = K L = 5$, and the desired length is $A C = 14 + 5 = 19$.

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