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To find the measure of arc \( AC \) in the circle, let's analyze the given information:

1. **The circle** has points \( A \), \( B \), and \( C \) lying on its circumference.
2. **\( \angle BAC = 44^\circ \)**, as indicated.

### Step-by-Step Solution:
In a circle, an inscribed angle (like \( \angle BAC \)) is equal to half the measure of the arc it intercepts. Here, \( \angle BAC \) intercepts arc \( AC \).

Using the inscribed angle theorem:
\[
\text{Measure of arc } AC = 2 \times \text{measure of } \angle BAC
\]

Substituting the given angle measure:
\[
\text{Measure of arc } AC = 2 \times 44^\circ = 88^\circ
\]

### Answer:
The measure of \( \overarc{AC} \) is **88°**.

So, the correct answer is:
- **D. 88°**

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Would you like a further breakdown of the inscribed angle theorem or have any other questions?

### Related Questions:
1. How does the inscribed angle theorem apply to other types of arcs?
2. What would the measure of arc \( BC \) be if \( \angle ABC \) is known?
3. How would the solution change if \( \angle BAC \) was given as 22°?
4. Can an inscribed angle be equal to its intercepted arc?
5. How would this problem change if the arc was a major arc instead?

### Tip:
Remember, for any inscribed angle, the intercepted arc is always twice the angle. This rule is very useful in solving problems involving circles.

Learn how to find the measure of arc AC in a circle using the Inscribed Angle Theorem. This problem involves identifying the relationship between an inscribed angle and its intercepted arc, a key concept in circle geometry. Suitable for students in Grades 8-10.

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