Relationship of Chord Lengths in a Circle with Parallel Chords

Consider a circle with center O and radius r. Two chords AB and CD are drawn such that they are parallel to each other and each chord is equidistant from the center O. The distance from O to chord AB is d, and the distance from O to chord CD is also d. If chord AB is longer than chord CD, which of the following statements is true regarding the lengths of the chords?

Let the lengths of chords AB and CD be represented as L_AB and L_CD, respectively. Recall that the length of a chord can be calculated using the formula:

$$ L = 2 imes ext{sqrt}(r^2 - d^2) $$

where r is the radius of the circle, and d is the distance from the center of the circle to the chord.