1. Lesson 19.4 – Segment Relationships in Circles
Please tear out pages

2. Chord – Chord Product Theorem

3. Example 1: Find the value of x and the length of each chord.
𝐶𝐸(𝐸𝐷)=𝐵𝐸(𝐸𝐴)
𝐶𝐷=8
Example 1:
6 2 =3𝑥
𝐴𝐵=7
12=3𝑥
𝑥=4
𝐺𝑖𝑣𝑒𝑛:𝐴𝐷=12
𝐸𝐷=9
𝐵𝐶=
3 9 =14𝑥
𝐴𝐷=12
27=14𝑥
𝑥= 14 27

4. Secant – Secant Product Theorem

5. Example 2: Find the value of x and the length of each secant segment.
𝐶𝐴(𝐵𝐴)=𝐸𝐴(𝐷𝐴)
𝐴𝐸=12
(5+𝑥)(5)=12(6)
𝐶𝐴=14 2 5
25+5𝑥=72
5𝑥=47
𝑥= 47 5 =9 2 5
𝐻𝐿(𝐽𝐿)=𝑁𝐿(𝑀𝐿)
𝐻𝐿=10
10(6)=(𝑥+𝑥+5)(5)
𝑁𝐿=12
60=(2𝑥+5)(5)
60=10𝑥+25
35=10𝑥
𝑥= = 7 2 =3 1 2

6. Secant – Tangent Product Theorem

7. Example 3: Find the value of x. 𝐷𝐵(𝐵𝐶)=𝐵 𝐴 2 (𝑥+2)(2)= (5) 2 2𝑥+4=25
2𝑥=21
𝑥= 21 2

8. On a bird-watching trip, you travel along a path tangent to a circular pond to a lookout station that faces a hawk’s nest. Given the measurements in the diagram on your bird-watching map, how far is the nest from the lookout station?
Example 4:
𝑥(25)= 100 2
25𝑥=10000
𝑥=400
400 𝑦𝑎𝑟𝑑𝑠 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑙𝑜𝑜𝑘𝑜𝑢𝑡 𝑠𝑡𝑎𝑡𝑖𝑜𝑛

9. Pg. 1049
#1-18 all
Assignment #41