1. Lesson 8-6: Segment Formulas
Special
Segments
Lesson 8-6: Segment Formulas

2. Intersecting Chords Theorem
Interior segments are formed by two intersecting chords.
Theorem:
If two chords intersect within a circle, then the product of the lengths of the parts of one chord is equal to the product of the lengths of the parts of the second chord. A B C D E a d b c
a • b = c • d
Lesson 8-6: Segment Formulas

3. Intersecting Chords Examples1. 2.
3x = 6*4
3x = 24
x = 8
2(x-2) = 12
2x – 4 = 12
2x = 16
x = 8 x 6 4 x 2 3 4 3 3.
x*x = 3*9
x2 = 27
x = sqrt(27)
= 3sqrt(3) 6 x 3 x 3
Lesson 8-6: Segment Formulas

4. Intersecting Secants/Tangents
Exterior segments are formed by two secants, or a secant and a tangent. D B C A D B A C E
Secant and a Tangent
Two Secants
Lesson 8-6: Segment Formulas

5. Intersecting Secants Theorem
If two secant segments are drawn to a circle from an external point, then the products of the lengths of the secant and their exterior parts are equal.
a • e = c • f
Lesson 8-6: Segment Formulas

6. Lesson 8-6: Segment Formulas
Example:
AB  AC = AD  AE D B A C E
4 cm
4  9 = 3  (3+x)
5 cm
3 cm
36 = 9 + 3x x
27 = 3x
X = 9 cm
Lesson 8-6: Segment Formulas

7. Secant and Tangent Theorem:
The square of the length of the tangent equals the product of the length of the secant and its exterior segment. D B C A
a2 = b • d a b c d
Lesson 8-6: Segment Formulas

8. Lesson 8-6: Segment Formulas
Example 1: D B C A x
3 cm
4 cm
Lesson 8-6: Segment Formulas

9. Lesson 8-6: Segment Formulas
Example 2:
102 = x(x+ 3x)
100 = x2 + 3x2
100 = 4 x2
25 = x2
x = 5 10 x 3x
Lesson 8-6: Segment Formulas