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.