2. Find m1 1. Find mXAB 42º 90º 3. Find mZ 70º Session 71 WARM UP A 222º D C 90º 3. Find mZ 55º Z Think!! 70º

Two chords intersect INSIDE the circle Type 1: a ab = cd d c b

Example 1: 9 12 6 3 x x 2 2 X = 3 X = 8 x 3 6 2 X = 1

Example 2: Find x 2x  3x = 12  8 8 12 2x 3x 6x2 = 96 x2 = 16 x = 4

EA * EB = EC * ED Two secents intersect Type 2: OUTSIDE the circle E A

7 (7 + 13) = 4 (4 + x) x = 31 140 = 16 + 4x 124 = 4x Example 3: B 13 A C x D 7 (7 + 13) = 4 (4 + x) x = 31 140 = 16 + 4x 124 = 4x

5 (5 + x) = 6 (6 + 8) x = 11.8 25+5x = 84 59 = 5x Example 4: B x A 5 D C 6 E 5 (5 + x) = 6 (6 + 8) x = 11.8 25+5x = 84 59 = 5x

Notice that on the tangent segment, the outside is the whole! Secant Segment External Segment Tangent Segment

Type 2 (with a twist): Secant and Tangent C B E A EA2 = EB * EC

Example 5: C B x 12 E 24 A 242 = 12 (12 + x) 576 = 144 + 12x x = 36

Example 6: 5 B E 15 C x A x2 = 5 (5 + 15) x2 = 100 x = 10

What you should know by now… Given two chords Given two secants OR a tangent and a secant