Presentation is loading. Please wait.

Presentation is loading. Please wait.

9.5: Segments of Tangents, Secants, and Chords

Similar presentations


Presentation on theme: "9.5: Segments of Tangents, Secants, and Chords"— Presentation transcript:

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. TOC

12


Download ppt "9.5: Segments of Tangents, Secants, and Chords"

Similar presentations


Ads by Google