1. 9.5: Segments of Tangents, Secants, and Chords

2. Segment Relationships
9.5 Segments of Tangents, Secants, and Chords
Segment Relationships
______ is a tangent segment
______ is a secant segment
_______ is an external secant segment
______ is a chord

3. 9.5 Segments of Tangents, Secants, and Chords
Theorems
If two segments are tangent to a circle from the same external point, then the segments are congruent.
Ex: Find x

4. Theorem
If two secants intersect outside a circle, 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 x Outside = Whole x Outside)

5. AE = 16, BE = 9, CE = 18, find DE A B E
C D

6. 9.5 Segments of Tangents, Secants, and Chords
Theorem
If a secant and a tangent intersect outside a circle, then the product of the lengths of the secant segment and its external segment equals the length of the tangent segment squared.
(Whole x Outside = Tangent Squared)

7. Example
C X E 10 D 8 B

8. Theorem
If two chords intersect inside a circle, then the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord.

9. Example

10. 9.5 Segments of Tangents, Secants, and Chords
Key Skills
Use segments formed by tangents, secants, and chords to solve problems.
Given: AB is tangent to
circle P at B, AH = 9,
HC = 16, and AG = 10
Find AB and AD.
To find AB: Whole  Outside = Tangent Squared
AC  AH = (25)(9) = (AB)2, so AB = 225 = 15.

11. 9.5 Segments of Tangents, Secants, and Chords
Key Skills
Use segments formed by tangents, secants, and chords to solve problems.
Given: AB is tangent to
circle P at B, AH = 9,
HC = 16, and AG = 10
Find AB and AD.
To find AD: Whole x Outside = Whole x Outside
AC  AH = AD  AG = (25)(9) = (AD)(10), so
AD = 22.5.
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