11.2.3 Segment Relationships in Circles (continued) Example 2 Environmental Application
The Chord-Chord Product Theorem is used in this application example to determine the diameter of a circle. It is given that one chord is the perpendicular bisector of a second chord. One segment length from each of the chords, 5 ft and 10 ft, are also given. PR is a diameter because it is perpendicular to and bisects QS . Substitute the given values into the equation for the Chord-Chord Product Theorem and solve for d . The solution yields d = 20. The diameter of the pond is the sum of the lengths of the two segments that make up the diameter, which is 25 ft.
Example 3 Applying the Secant-Secant Product Theorem
If two secants intersect in the exterior of a circle, then the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment. (whole · outside = whole · outside) The Secant-Secant Product Theorem is used in this example to determine the lengths of secant segments. The lengths of three of the segments formed by two secants intersecting a circle are given. Substitute the given values into the equation for the Secant-Secant Product Theorem and solve for x . The solution yields x = 4. Therefore, BC = 5, AC = 12, DC = 6, and EC = 10.
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