Question

Math

Posted 6 months ago

```
Angle $C$ is inscribed in circle $O$.
$\overline{A B}$ is a diameter of circle $O$.
What is the measure of $\angle A$ ?
$\mathrm{O}$
```

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Answer from Sia

Posted 6 months ago

Solution by Steps

step 1

Recognize that in a circle, an inscribed angle is half the measure of its intercepted arc

step 2

Identify that the intercepted arc for $\angle C$ is the arc from point A to point B, which is a semicircle

step 3

Since $\overline{AB}$ is a diameter, the arc measures $180^\circ$

step 4

Calculate the measure of $\angle A$ by using the inscribed angle theorem, which states that the angle is half the measure of the intercepted arc

step 5

Therefore, the measure of $\angle A$ is $\frac{1}{2} \times 180^\circ = 90^\circ$

1 Answer

The measure of $\angle A$ is $90^\circ$.

Key Concept

Inscribed Angle Theorem

Explanation

The inscribed angle theorem states that an inscribed angle is half the measure of its intercepted arc. Since the intercepted arc is a semicircle (180 degrees), the inscribed angle is 90 degrees.

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