1. Bellwork
1) (x+3)(x+7)
2) (2x+4)(x-4)

2. Segment Lengths in Circles
10.5
Segment Lengths in Circles

3. Segments of Chord 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.
EA EB = EC ED D A C B E
*We can set up a 
proportion to find the 
missing length!

4. D A C B E 9 3 x 6

5. Example a) D A C B E 12 8 6 x

6. C 8 A x E 2x 9 B D

7. C 15 A 10 E
x+1 x D B

8. Example e)
x+1 C
x+2 E
x+3 A
x+5 D B

9. external secant segment
When two chords intersect in a circle, each chord is divided into 
two segment called segments of the chord.
A secant segment is a segment that contains a chord of a circle, and exactly one endpoint outside the circle.
The part of the secant that is outside of the circle is called an 
external segment.
external secant segment
tangent segment
secant segment
touches 2 places
touches 1 place

10. 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. E A B C D
EA EB = EC ED

11. E A B C D 11 9 x 10

12. Example b) E A B C D 4 x 2 4

13. You try b) A B 8 6 E x 7 D C

14. Example b) A 72 B 2 E 40 D C 78

15. Example f) E A B C D
x+3
x+1
x+2 2