segment relationships in circles
TRANSCRIPT
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