Archaeologists have found a piece of an artifact, which is likely to be the edge of a circular object. The chord connecting the endpoints of the arc on the intact part of the edge is $16 \mathrm{~cm}$, and the height of the circular segment defined by the chord and the arc is $2 \mathrm{~cm}$. What was the diameter of the disc?
Let $A$ and $B$ be the endpoints of the chord, $O$ the center of the circle, and $C$ the midpoint of $AB$.

![](https://cdn.mathpix.com/cropped/2024_05_02_5a7a4492261c7e7ace83g-1.jpg?height=385&width=398&top_left_y=225&top_left_x=847)

Applying the Pythagorean theorem to triangle $OCB$:

$$
r^{2}=8^{2}+(r-2)^{2}
$$

From this, $2r=34 \text{ cm}$.