Explanation:

- Let the circles have radii \( r_1 = 18 \) cm and \( r_2 = 16 \) cm.

- Let the distance between centers be \( d \), and let the common chord be of length 19.2 cm.

- The common chord is perpendicular to the line joining the centers and divides it into two segments.

- The distances from the centers to the chord are \( \sqrt{r_1^2 - (\frac{l}{2})^2} \) and \( \sqrt{r_2^2 - (\frac{l}{2})^2} \), where \( l = 19.2 \) cm.

- So, \( d = \sqrt{r_1^2 - (l/2)^2} + \sqrt{r_2^2 - (l/2)^2} \)

- Calculate \( l/2 = 9.6 \) cm

- \( \sqrt{18^2 - 9.6^2} = \sqrt{324 - 92.16} = \sqrt{231.84} \approx 15.23 \) cm

- \( \sqrt{16^2 - 9.6^2} = \sqrt{256 - 92.16} = \sqrt{163.84} \approx 12.8 \) cm

- So, \( d \approx 15.23 + 12.8 = 28.03 \) cm, rounding to nearest integer, \( 28 \) cm.

- Option 1: 23 cm ? Too small.

- Option 2: 28 cm Correct; matches our result

- Option 3: 20 cm ? Too small.

- Option 4: 35 cm ? Too large.

Option:2- 28 cm is the correct answer.