The diagram shows a circle with center O, and the diameter is AB. Points A, B, and C lie on the circumference. Let's break down the questions based on the image:

(a) Write down the mathematical name of the line AC.

Given that A, B, and C are points on the circumference and AC connects two points on the circle, the mathematical name for the line is a chord.

(b) Find the value of x.

For the second part, since we know angle ACB is an inscribed angle subtended by the diameter AB, by the Inscribed Angle Theorem, an angle subtended by a diameter is always a right angle (90°). Hence, ∠ACB = 90°. The value of x is likely referring to an angle, and we can use this information to find x, if needed.

Final answers:

(a) Chord AC
(b) x = 90° because ∠ACB is subtended by the diameter AB and is a right angle.

Would you like further details on this explanation or have any additional questions? Here are some related topics:

1. What is the Inscribed Angle Theorem and how does it work in circles?
2. Can the Inscribed Angle Theorem be applied to other types of geometric figures?
3. What other properties does a chord in a circle have?
4. How can you calculate the area of a circle given the diameter?
5. What is the significance of a diameter in a circle's properties?

Tip: The Inscribed Angle Theorem is a key concept when working with angles in circles—always remember that an angle subtended by a diameter will always be a right angle!