1. **Finding CD (Length of a Segment):**
- CD is the length of the line segment connecting points C and D.
- To find CD, we need to use the Pythagorean Theorem because segment CD is the hypotenuse of a right triangle with sides 6 cm and 8 cm (points C, D, and the center of the circle form a right triangle).
- Using the Pythagorean Theorem: \(a^2 + b^2 = c^2\), where a and b are the legs of the triangle, and c is the hypotenuse.
- Substituting the values: \(6^2 + 8^2 = CD^2\)
- \(36 + 64 = CD^2\)
- \(100 = CD^2\)
- Taking the square root of both sides, we get \(CD = 10\) cm. So, the length of CD is 10 cm.
2. **Finding Angle C (Central Angle):**
- Angle C is a central angle in the circle, and it intercepts an arc whose measure is 120°.
- In a circle, a central angle is equal in measure to its intercepted arc.
- Therefore, Angle C is 120°.
In conclusion:
- CD (the length of segment CD) is 10 cm.
- Angle C is 120°.
