When two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal. That means if we have two chords divided into segments, the relationship can be expressed as:
\[ (a)(b) = (c)(d) \]
where \(a\) and \(b\) are the lengths of the segments of the first chord, and \(c\) and \(d\) are the lengths of the segments of the second chord.
In the problem, we know:
- The first chord is divided into segments measuring 8 units and 9 units (let's assign \(a = 8\) and \(b = 9\)).
- The second chord is divided into one segment measuring 3 units (let's assign \(c = 3\)), and we need to find the length of the other segment (let's assign this unknown segment as \(d\)).
Using the property of intersecting chords, we can write the equation:
\[ (8)(9) = (3)(d) \]
Calculating \(8 \times 9\):
\[ 72 = 3d \]
Now, solve for \(d\):
\[ d = \frac{72}{3} = 24 \]
So the measure of the other segment is 24 units.
The correct answer is:
E. 24 units.
1 answer