Final answer:
The distance from the center of the circle to the chord is found using the Pythagorean theorem, resulting in approximately 16.17 cm.
Step-by-step explanation:
To find the distance of a chord from the center of a circle, we can use the properties of right triangles and Pythagoras' theorem. Given that the radius (r) of the circle is 16.8 cm and the length of the chord (c) is 9.1 cm, we can form a right triangle where the distance from the center to the chord (d) is one leg, and half the chord length (4.55 cm) is the other leg, while the radius (16.8 cm) is the hypotenuse. Applying the Pythagorean theorem:
- r2 = d2 + (c/2)2
- 16.82 = d2 + 4.552
- d2 = 16.82 - 4.552
- d = √(16.82 - 4.552)
- d = √(282.24 - 20.7025)
- d = √261.5375
- d ≈ 16.17 cm
Therefore, the distance of the chord from the center of the circle is approximately 16.17 cm.