3. In triangle $A B C$, side $B C$ is 18 cm. The perpendicular $D F$, drawn from the midpoint of side $A B$ - point $D$, intersects side $B C$ at point $F$. Find the perimeter of triangle $A F C$, if side $A C$ is $9 \, \text{cm}$.
# Solution:

![](https://cdn.mathpix.com/cropped/2024_05_06_a3feddd7c418bd26b633g-1.jpg?height=280&width=352&top_left_y=1873&top_left_x=338)

Triangle $ABF (BF = AF)$ is isosceles, since $DF \perp AB$, and $D$ is the midpoint of $AB$. $P_{AFC} = AF + FC + AC = BF + FC + AC = BC + AC = 27 \text{ cm}$.

Answer: 27 cm.