Angle \[C\] is inscribed in circle \[O\].
\[\overline{AB}\] is a diameter of circle \[O\].

**What is the measure of \[\angle A\]?**

In this scenario, where \(\overline{AB}\) is a diameter of the circle and \(\angle C\) is inscribed in the circle with vertex \(C\) on the circle, the measure of \(\angle A\) can be determined using the properties of inscribed angles in a circle.

**Key property:**

- An angle inscribed in a semicircle (i.e., an angle subtended by the diameter) is a right angle.

Since \(\overline{AB}\) is a diameter, and \(\angle C\) is an inscribed angle with vertex \(C\) on the circle, \(\angle C\) subtends the arc \(\overline{AB}\), which is a semicircle.

Therefore, \(\angle C\) is a right angle, i.e., \(\angle C = 90^\circ\).

**However**, the problem asks for the measure of \(\angle A\). Without more information about the specific position of points \(A\), \(B\), and \(C\) in the circle, and considering that \(\angle A\) could refer to different angles depending on the triangle configuration, we need to clarify. 

If we are dealing with a triangle \(ABC\) where \(C\) is inscribed and \(AB\) is the diameter, \(\angle A\) would typically be calculated based on the specific placement of \(C\). 

If \(C\) is anywhere else on the circle and if \(AB\) is the diameter, \(\angle A\) is not directly given by the provided information. Further specifics are needed to find \(\angle A\).

**Given the standard situation** (if \(\angle A\) is part of a triangle like \(\angle CAB\)), it can be calculated using the known inscribed angle properties and might depend on \(C\)'s position.

Would you like to clarify or get more details on this scenario? Here are some related questions that might help:

1. How do you calculate angles subtended by chords that are not diameters?
2. What happens if \(\angle A\) is given to be part of another triangle in the same circle?
3. Can an angle subtended by a diameter ever be something other than \(90^\circ\)?
4. How does the position of point \(C\) affect the inscribed angle?
5. How do you apply the properties of inscribed angles to solve for unknown angles?

**Tip:** When working with circles, always consider whether the angle is subtended by a diameter, as this immediately tells you it's a right angle.

Learn how to calculate angle A in circle O, where angle C is inscribed and AB is a diameter. Understand the properties of inscribed angles in a circle and their relationships to diameters. Suitable for Grades 7-9 students studying circle geometry.

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