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Two secants intersect OUTSIDE the circle E A B C D EA • EB = EC • ED

x = 31 7 (7 + 13) = 4 (4 + x) 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

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

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

Secant and Tangent C B E A EA2 = EB • EC

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

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

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

Work p. 632 10 - 27

Homework: Worksheet 10.5 B