NAME
DATE
PERIOD
10-3 HTM Arcs and Chords
Arcs and Chords Points on a circle determine both chords and arcs. Several
properties are related to points on a circle. In a circle or in congment circles, two
minor arcs are congruent if and only if their corresponding chords are congruent.
Example: In QK, AB = CD. Find AB.
AB and CD are congruent arcs, so the corresponding chords AB and CD are congruent.
AB = CD
Definition of congment segments
i
So, AD = 8 ( £ ) o r 4 .
Exercises
ALGEBRA Find the value of jc in each circle.
1.
s \
3.
R
0»
RS = TV if and only if RS
s TV.
10-3
NTM
(continued)
Diameters and Chords
' • In a circle, if a diameter (or radius) is perpendicular
to a chord, then it bisects the chord and its arc.
• In a circle, the perpendicular bisector of a chord is
the diameter (or radius).
• In a circle or in congruent circles, two chords are
congruent if and only tfthey are equidistantfrom the
center.
\iWz
lis,
then M
= XB
and
AW
sWi.
\f OX =0Y, then AB^RS.
\fAB
= RS,
then AB
and RS are equidistant from point O.
Example: In QO, CD ± OE, OD = 15, and CD = 24. Find OE.
A diameter or radius perpendicular to a chord bisects the chord, so ED is half of CD.
DD = i(24)
= 12
Use the Pythagorean Theorem to find OE in AGED.
(OEY + (EDf = (0D)2
(0Ey+JW=tl5
(pEY = 61
OE = R
Exercises
_a 0 P , the radius is 13 and RS = 24. Find each measure.
Round to the nearest hundredth.
2. PT -jJl
3. TQ
^8]
13
In QA, the diameter is 12, CD = 8, and mCD = 90. Find each measure.
Round to the nearest hundredth.
4. mDE r
S.FD
B
a
cm ^- zo
/\F'^o
. • -T.lnGi?, 7'S'=21and
8. In OQ, CD = CB,GQ=x + 5 and
Dg = 3jc-6. What is X?
DF=3JC. Whatisjc?
S
T
U
ck
h^
3K-LI
^3