1. Day 3

2. Segment Relationships
One Secant and
one Tangent Intersect!
Two Chords Intersect! A B C D E B A C D
𝐴𝐸 ∗ 𝐸𝐶 = 𝐷𝐸 ∗ 𝐸𝐵
𝐴𝐷 ∗ 𝐵𝐷 = ( 𝐶𝐷 ) 2
Segment Relationships
Two Secants Intersect! A C B F G
𝐴𝐵 ∗ 𝐹𝐵 = 𝐶𝐵 ∗ 𝐺𝐵

3. EX 6: Find 𝐴𝐸 if 𝐸𝐵 =8, 𝐷𝐸 =6, and 𝐸𝐶 =12C B F G A B C D E
𝐴𝐸 ∗ 𝐸𝐶 = 𝐷𝐸 ∗ 𝐸𝐵
𝐴𝐸 ∗12=6∗8
𝐴𝐸 ∗12=48
EX 8: Find 𝐴𝐵 if 𝐶𝐵 =10,
𝐺𝐵 =5, and 𝐹𝐵 =4
𝐴𝐸 =4
𝐴𝐵 ∗ 𝐹𝐵 = 𝐶𝐵 ∗ 𝐺𝐵
EX 7: Find 𝐶𝐷 if 𝐴𝐵 =5, 𝐵𝐷 =4
𝐴𝐵 ∗4=10∗5
𝐴𝐷 ∗ 𝐵𝐷 = ( 𝐶𝐷 ) 2 B A C D
𝐴𝐵 ∗4=50
9∗4= ( 𝐶𝐷 ) 2
𝐴𝐵 =12.5
36= ( 𝐶𝐷 ) 2
6= 𝐶𝐷

4. If two chords are congruent, then the arcs are congruentB C
If two chords are congruent, then the arcs are congruent
𝑖𝑓 𝐴𝐵 ≅𝐶𝐵 𝑡ℎ𝑒𝑛 𝐴𝐵 ≅ 𝐶𝐵 A C B D E
If a radius or diameter is perpendicular to a chord, then the radius bisects the chord, and the arc. 𝑖𝑓 𝐴𝐷 𝑖𝑠 𝑝𝑒𝑟𝑝𝑒𝑛𝑖𝑐𝑢𝑙𝑎𝑟 𝑡𝑜 𝐵𝐶 𝑡ℎ𝑒𝑛 𝐵𝐷 ≅ 𝐶𝐷 and 𝐵𝐸 ≅ 𝐸𝐶 A C B D E F G H I
Two chords are congruent, if and only if they are equidistant from the center. 𝐺𝐻 ≅ 𝐵𝐶 𝑖𝑓 𝑎𝑛𝑑 𝑜𝑛𝑙𝑦 𝑖𝑓 𝐴𝐸 ≅ 𝐴𝐸

5. A line is tangent to a circle if and only if
it is perpendicular to a radius drawn at the point of tangency
𝐶𝐴 𝑖𝑠 𝑡𝑎𝑛𝑔𝑒𝑛𝑡 𝑡𝑜 𝑐𝑖𝑟𝑐𝑙𝑒 𝑇.
𝐴 𝑖𝑠 𝑡ℎ𝑒 𝑝𝑜𝑖𝑛𝑡 𝑜𝑓 𝑡𝑎𝑛𝑔𝑒𝑛𝑐𝑦 A C T Z X Y
If two segments from the same exterior point are tangent to a circle, then they are congruent
𝑌𝑍 𝑎𝑛𝑑 𝑌𝑋 𝑎𝑟𝑒 𝑡𝑎𝑛𝑔𝑒𝑛𝑡 𝑡𝑜 𝑡ℎ𝑒 𝑐𝑖𝑟𝑐𝑙𝑒.
𝑇ℎ𝑢𝑠. 𝑌𝑍 ≅ 𝑌𝑋