6.6 Finding Segment Lengths

ab = cd Chord-Chord Rule: Two chords intersect INSIDE the circle a d c

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

Secant-Secant Rule: OW-OW

EA • EB = EC • ED Two secants intersect Secant-Secant Rule: OUTSIDE the circle Secant-Secant Rule: 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

When A secant and tangent originate from the same Secant-Tangent Rule: When A secant and tangent originate from the same point OUTSIDE the circle, use O ●W = O ●W.

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

A secant and tangent originate from the same point Secant-Tangent Rule: A secant and tangent originate from the same point OUTSIDE the circle 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, USE Given two secants OR a tangent and a secant, USE What you should know by now… Given two chords, USE Given two secants OR a tangent and a secant, USE