10.5: Find Segment Lengths in Circles GEOMETRY: Chapter 10 10.5: Find Segment Lengths in Circles

Theorem 10.15 Segments of Chords Theorem If two chords intersect in the interior of a circle, then 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. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 689.

Ex.1: Find RT and SU. Answer: RT = 13; SU = 15 Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 681.

Tangents and Secants A secant segment is a segment that contains a chord of a circle, and has exactly one endpoint outside the circle. The part of a secant segment that is outside the circle is called an external segment. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 681.

Theorem 10.16 Segments of Secants Theorem If two secant segments share the same endpoint outside 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. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 690.

Ex. 2: Find the value of x. Answer: 5 Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 690.

Theorem 10.17 Segments of Secants and Tangents Theorem If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 691.

Use the figure to find AB. Ex. 3: Use the figure to find AB. Answer: 20 Images taken from: Geometry. McDougal Littell: Boston, 2007. P.691.

Answer: about 1106 miles Ex. 4: Images taken from: Geometry. McDougal Littell: Boston, 2007. P.692.

10.5, p. 632, #10-25 all (16 questions)