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

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




In a circle, an inscribed angle that subtends a diameter is always a right angle (90°). This is due to the fact that the angle inscribed in a semicircle is always a right angle.

Given that \( \overline{AB} \) is the diameter of circle \( O \) and angle \( C \) is inscribed, with point \( C \) lying on the circle, the measure of angle \( A \) (which is actually the measure of angle \( \angle ACB \) because \( \overline{AB} \) is the diameter) is:

\[
\angle A = 90^\circ
\]

This follows from the property of the circle that states an inscribed angle that subtends a semicircle is always a right angle.

Would you like further details or have any other questions?

Here are 8 relative questions to explore this topic further:
1. What is the definition of an inscribed angle in a circle?
2. Why does an inscribed angle subtending a semicircle always measure 90 degrees?
3. How can the inscribed angle theorem be used to find other angles in the circle?
4. What is the difference between a central angle and an inscribed angle in a circle?
5. How can you prove that an inscribed angle subtending a diameter is a right angle?
6. What are the properties of a diameter in relation to the circle's other chords and secants?
7. How do you calculate the arc length corresponding to a given central angle?
8. Can the property of the angle subtended by a diameter be generalized to other polygons inscribed in a circle?

**Tip:** Remember that in any circle, the angle subtended by a chord at the center is twice the angle subtended by the same chord at any point on the circle.

Explore the concept of inscribed angles in a circle with diameter AB. Learn why an inscribed angle subtending a diameter is always 90 degrees and how this relates to circle geometry. Suitable for high school students.

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