Name: Lido Date: Period:Notes-14.4

Segment Relationships in Circles

Chord — Chord Theorem

If two chords intersect inside a circle, then the roductS of the lengths c

of the segments of the chords are equal.

D

EX 1: Find the value of x and the length of each chord.

a) c CE•ED = BE b)1 HG.éJ=kG 61

96 x

3

x E 2 6 12: xK 8

D

-a part of a secant line with at least one point on the circle.

Secant — Secant Product Theorem

If two secants intersect in the exterior of a circle, then the productof the lengths of one secant segment and its external segmentequals the product of the lengths of the other secant segment andits external segment.

cCEDE =

EX 2: Find the value of x and the length of each secant segment

RP a) b) = (JPeTPCh'bR 14 •62

x c6 p

5 8

72 = osx S 76 6 x

Name: Date: Period:Notes-14.4

- a segment of a tangent line with exactly one endpoint on the circle.

Secant — Tangent Theorem

If a secant and a tangent intersect in the exterior of a circle, then the

product of the lengths of the secant segment and its external segment

equals the length of the tangent segment squared. c

Dc iAC ø ßc

EX 3: Find the value of x.

a) b) c hC•BC =DCt6

5 (2+x)2 = g 2

c x2 x

Practice Problems:

1. Given AD = 12. Find the Value of x and the 2. Find the value of x and the length of each

length of egch chord. secant segment.

5.414

5

x 4S x

c

3. Find the value of the variable.

5

c2 x