Day 3

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

EX 6: Find 𝐴𝐸 if 𝐸𝐵 =8, 𝐷𝐸 =6, and 𝐸𝐶 =12 C 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

If two chords are congruent, then the arcs are congruent B 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

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