9 5 Segments of Tangents Secants and Chords

9. 5 Segments of Tangents, Secants, and Chords Theorems If two segments are tangent

Theorem If two secants intersect outside a circle, the product of the lengths of

9. 5 Segments of Tangents, Secants, and Chords Theorem If a secant and a

Example C X E 10 D 8 B Copyright © by Holt, Rinehart and

Theorem If two chords intersect inside a circle, then the product of the lengths

Example Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

9. 5 Segments of Tangents, Secants, and Chords Key Skills Use segments formed by

Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

Slides: 12

Download presentation

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 Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

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 Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

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) Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

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) Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

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. Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

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. Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

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 Copyright © by Holt, Rinehart and Winston. All Rights Reserved.