Petr drew a regular hexagon whose vertices lay on a circle with a circumference of $16 \mathrm{~cm}$. Then, from each vertex of this hexagon, he drew a circle that passed through the two adjacent vertices. This resulted in a figure as shown in the following image.

Determine the perimeter of the marked flower.

(E. Novotná)

![](https://cdn.mathpix.com/cropped/2024_04_17_3ab73cf5e47d7567d598g-2.jpg?height=551&width=596&top_left_y=1518&top_left_x=730)

Hint. Look for (and justify) congruent parts of the image.
All circles in the previous image are congruent to each other. Therefore, the marked segments in the following image are also congruent to each other, as are the corresponding arcs.

![](https://cdn.mathpix.com/cropped/2024_04_17_3ab73cf5e47d7567d598g-3.jpg?height=414&width=366&top_left_y=184&top_left_x=845)

The two arcs forming the edge of each petal have twice the length of the corresponding arc of the original circle from which it was created. Therefore, the perimeter of the flower is twice the length of the original circle, i.e., \(32 \mathrm{~cm}\).