Geometry Regents Practice Exam

To find the measurement of two chords that intersect each other within a circle, the correct formula involves setting the products of the segments of each chord equal to one another. The reason option B is correct is that it reflects the property of intersecting chords: the product of the lengths of the two segments of one chord is equal to the product of the lengths of the two segments of the other chord. This can be expressed mathematically as:

(part of chord 1) * (part of chord 1) = (part of chord 2) * (part of chord 2)

This means that if you have one chord divided into two segments (let's call them part chord 1) and another chord also divided into two segments (part chord 2), the equation ensures that the relationship between the segments is preserved when the chords intersect.

Understanding why the other choices do not represent the correct relationship is valuable, too. For example, options that suggest addition (like the first choice) or division (like the fourth choice) do not accurately reflect the geometric properties involving intersecting chords. Multiplying segments provides a relationship necessary for solving various problems dealing with circle geometry and segments formed by chords.