Sure, let's break this down step by step.
When two chords intersect each other inside a circle, they form an angle at the point of their intersection. This angle is related to the arcs that are intercepted by the chords.
### Important Fact:
The measure of an angle formed by two intersecting chords is equal to half the sum of the measures of the intercepted arcs.
This can be stated mathematically as:
[tex]\[ \text{Measure of the angle} = \frac{1}{2} (\text{Measure of Arc 1} + \text{Measure of Arc 2}) \][/tex]
### Let's assume:
- Arc [tex]\( \overset{\frown}{AB} \)[/tex] is the arc intercepted by one of the intersecting chords.
- Arc [tex]\( \overset{\frown}{CD} \)[/tex] is the arc intercepted by the other chord.
### Step-by-Step Solution:
1. Identify the intercepted arcs:
- Determine which arcs are being intercepted by the intersecting chords. These are the arcs that lie within the angle formed at the intersection point.
2. Sum the measures of intercepted arcs:
- Find the measures of these intercepted arcs. Let’s represent them as [tex]\( m(\overset{\frown}{AB}) \)[/tex] and [tex]\( m(\overset{\frown}{CD}) \)[/tex].
3. Calculate the measure of the angle:
- According to the property, the measure of the angle formed by the intersecting chords is half the sum of the measures of the intercepted arcs.
- So, if the angle formed is [tex]\( \theta \)[/tex], then:
[tex]\[
\theta = \frac{1}{2} (m(\overset{\frown}{AB}) + m(\overset{\frown}{CD}))
\][/tex]
### Conclusion:
The measure of an angle formed by intersecting chords is half the sum of the measures of the intercepted arcs.
Therefore, the correct option is:
A. half
This means the angle formed by the intersecting chords is exactly half of the total measure of the intercepted arcs.
