Answer: The smallest value is $2 \pi \sqrt{10}$ cm. In the answer, we write 20, since $2 \pi \sqrt{10} \approx 19.8691 \ldots$
3. The area of triangle $\triangle A B C$ is 10 cm $^{2}$. What is the smallest value in centimeters that the circumference of the circle circumscribed around triangle $\triangle A B C$ can take, given that the midpoints of the heights of this triangle lie on the same line? If the answer is not an integer, round it to the nearest integer.