To apply the intersecting chords theorem, you need to multiply the lengths of the segments of one chord and equate that product to the product of the segments of the other chord.

The intersecting chords theorem states that when two chords intersect within a circle, the products of the lengths of the segments of each chord are equal. For example, consider a circle with two chords, $AB$ and $CD$, that intersect at point $E$. According to the theorem, the relationship can be expressed as:

To effectively use this theorem, first identify the intersection point where the chords meet. Then, measure or note the lengths of the segments formed by this intersection. For instance, if chord $AB$ is divided into segments $AE$ and $EB$, and chord $CD$ is divided into segments $CE$ and $ED$, you would measure the lengths of these segments.

As an example, suppose we have the following segment lengths: $AE = 3 \, \text{cm}$, $EB = 4 \, \text{cm}$, $CE = 2 \, \text{cm}$, and $ED = x \, \text{cm}$. You would set up the equation based on the theorem:

Solving this gives:

From this, we can determine that:

This indicates that segment $ED$ is $6 \, \text{cm}$ long. This method is particularly useful for finding unknown lengths in problems involving intersecting chords within a circle.