What is the product relationship for the lengths of two intersecting chords?

The product relationship of two intersecting chords states that when two chords intersect each other inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. This is mathematically represented as follows: if one chord is divided into two segments, say 'a' and 'b', and the other chord is divided into segments 'c' and 'd', then the equation a × b = c × d holds true. This relationship is derived from the properties of circle geometry and helps in solving various problems involving chords.

This principle is crucial because it allows for the determination of lengths of segments knowing the lengths of the other segments, thus proving useful in many geometric contexts. The other options don't accurately describe this fundamental property of intersecting chords.