Chapter 10 6 Notes Find Segment Lengths in

Chords • When two chords intersect in the interior of a circle, each chord

Ex. 1: Find ML and JK. Ex. 2: Find RT and SU.

Tangents and Secants • A secant segment is a segment that contains a chord

• Theorem 10. 15 Segments of Secants Theorem: If two secant segments share

Ex. 4: What is the value of x? • Theorem 10. 16 Segments of

• Determine which theorem you would use to find x. Then find the

Ex. 12: Suppose the Space shuttle is positioned at point S, 150 miles above

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Chapter 10. 6 Notes: Find Segment Lengths in Circles Goal: You will find segment lengths in circles.

Chords • When two chords intersect in the interior of a circle, each chord is divided into two segments that are called segments of the chord. • Theorem 10. 14 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.

Ex. 1: Find ML and JK. Ex. 2: Find RT and SU.

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.

• Theorem 10. 15 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. Ex. 3:

Ex. 4: What is the value of x? • Theorem 10. 16 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.

Ex. 5: Find RS. Ex. 6: Find AB.

• Determine which theorem you would use to find x. Then find the value of x. Ex. 7: Ex. 8: Ex. 9: Ex. 10:

• Determine which theorem you would use to find x. Then find the value of x. Ex. 11:

Ex. 12: Suppose the Space shuttle is positioned at point S, 150 miles above the Earth. What is the length of ES from the Earth to the shuttle? (The radius of the Earth is about 4000 miles. )