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To find the measure of the indicated arc \(\overarc{AC}\), let's analyze the given information:

1. **Central Angle:** The angle at the center of the circle (which is the angle subtended by arc \(BC\)) is given as \(145^\circ\).
2. **Inscribed Angle:** The angle \(\angle BAC\) is \(47^\circ\).

### Key Concept:
- The measure of an **inscribed angle** is always half the measure of the arc it subtends.
  
Given that \(\angle BAC\) is \(47^\circ\), it subtends the arc \(AC\). Therefore, the arc \(\overarc{AC}\) is:
\[
\overarc{AC} = 2 \times \angle BAC = 2 \times 47^\circ = 94^\circ
\]

Thus, the measure of the indicated arc \(AC\) is \(94^\circ\).

Would you like any further details or have any questions?

### Related Questions:
1. How would you calculate the measure of arc \(BC\)?
2. What is the relationship between central angles and their subtended arcs?
3. If \(\overarc{AB}\) is \(145^\circ\), what is the measure of angle \(\angle ACB\)?
4. What is the measure of angle \(\angle BCA\) in triangle \(ABC\)?
5. How do inscribed angles behave in semicircles?

### Tip:
When dealing with inscribed angles in a circle, always remember that they are half the measure of the arc they intercept. This is a powerful property for solving many problems involving circles.

Learn how to find the measure of the indicated arc \(\overarc{AC}\) in a circle using central and inscribed angles. This problem involves circle geometry and the relationship between inscribed angles and their corresponding arcs. Suitable for students in Grades 7-9.

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