Explanation:

- Given two circles with radii 18 cm and 16 cm.

- The length of the common chord is 19.2 cm.

- To find the distance between the centers of the circles, use the formula:

$$

d = \sqrt{r_1^2 + r_2^2 - \text{(length of chord)}^2}

$$

where $r_1$ and $r_2$ are the radii of the circles.

- Plug in the values:

$$

d = \sqrt{18^2 + 16^2 - 19.2^2}

$$

$$

d = \sqrt{324 + 256 - 368.64}

$$

$$

d = \sqrt{211.36}

$$

$$

d \approx 14.54 \text{ cm}

$$

- The correct distance is not close to 1, 23, 28, or 35 cm.

- Option:3, 20 cm would be a better estimated result considering all options, though not exact.

.