Lesson 19.4 – Segment Relationships in Circles Please tear out pages 1041-1054

Chord – Chord Product Theorem

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=14 14 27 3 9 =14𝑥 𝐴𝐷=12 27=14𝑥 𝑥= 14 27

Secant – Secant Product Theorem

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= 35 10 = 7 2 =3 1 2

Secant – Tangent Product Theorem

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

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

Pg. 1049 #1-18 all Assignment #41