Ci
r
cle
s
—
F
u
ll De
pt
h S
tu
d
y
G
u
ide
(
NC Ma
t
h
2
CDM
)
1
.
VOCABULARY
—
Dee
p
Di
v
e
Radi
us
(
r
)
Seg
m
e
nt
f
rom
t
he
ce
nt
e
r
to
a
ny
po
i
nt
ON
t
he ci
r
cle
.
E
v
e
ry
r
adi
us
i
n
a gi
v
e
n
ci
r
cle i
s
t
he
s
a
m
e le
n
g
t
h
—
t
hi
s
i
s
ac
tu
all
y
t
he de
fin
i
t
i
on
o
f a ci
r
cle
(
t
he
s
e
t
o
f all
po
i
nts
e
qu
idi
st
a
nt
f
rom
a ce
nt
e
r
po
i
nt
).
Dia
m
e
t
e
r
(
d
)
A ch
or
d
t
ha
t
p
a
ss
e
s
THROUGH
t
he ce
nt
e
r
,
c
onn
ec
t
i
n
g
two
po
i
nts
on
t
he ci
r
cle
.
I
t
'
s
t
he
l
on
ge
st
poss
ible ch
or
d i
n
a
ny
ci
r
cle
.
Rela
t
i
ons
hi
p
:
d
=
2r
,
or
r
=
d
/
2
Thi
s
r
ela
t
i
ons
hi
p
s
h
ows
up
c
onst
a
nt
l
y
—
if a
pro
ble
m
gi
v
e
s
you
t
he dia
m
e
t
e
r
,
you
al
most
al
w
a
ys
n
eed
to
hal
v
e i
t
bef
or
e
us
i
n
g a
r
adi
us
-
ba
s
ed f
ormu
la
(
like a
r
c le
n
g
t
h
or
s
ec
tor
a
r
ea
).
Ch
or
d
A
ny
s
eg
m
e
nt
c
onn
ec
t
i
n
g
two
po
i
nts
on
t
he ci
r
cle
.
A dia
m
e
t
e
r
i
s
a
sp
ecial ch
or
d
(
i
t
p
a
ss
e
s
t
h
rou
gh
t
he ce
nt
e
r
);
most
ch
or
d
s
d
on
'
t
.
Ke
y
prop
e
rty
:
The
p
e
rp
e
n
dic
u
la
r
d
r
a
wn
f
rom
t
he ce
nt
e
r
o
f a ci
r
cle
to
a ch
or
d al
w
a
ys
bi
s
ec
ts
t
ha
t
ch
or
d
(
c
uts
i
t
e
x
ac
t
l
y
i
n
half
).
Thi
s
s
h
ows
up
i
n
pro
ble
ms
t
ha
t
gi
v
e
you
a ch
or
d le
n
g
t
h
a
n
d a
s
k f
or
i
ts
di
st
a
n
ce f
rom
t
he ce
nt
e
r
.
Ta
n
ge
nt
A li
n
e
t
ha
t
i
nt
e
rs
ec
ts
a ci
r
cle a
t
e
x
ac
t
l
y
on
e
po
i
nt
(
t
he
po
i
nt
o
f
t
a
n
ge
n
c
y
).
Ke
y
prop
e
rty
:
A
t
a
n
ge
nt
li
n
e i
s
al
w
a
ys
p
e
rp
e
n
dic
u
la
r
to
t
he
r
adi
us
d
r
a
wn
to
t
he
po
i
nt
o
f
t
a
n
ge
n
c
y
.
Thi
s
c
r
ea
t
e
s
a
90
°
a
n
gle
,
w
hich i
s
a h
u
ge cl
u
e i
n
diag
r
a
ms
—
if
you
s
ee a
t
a
n
ge
nt
a
n
d a
r
adi
us
m
ee
t
i
n
g
,
t
ha
t
'
s
a
r
igh
t
a
n
gle
you
ca
n
us
e
w
i
t
h
t
he P
yt
hag
or
ea
n
t
he
or
e
m
.
T
wo
t
a
n
ge
nt
s
eg
m
e
nts
d
r
a
wn
f
rom
t
he
s
a
m
e e
xt
e
rn
al
po
i
nt
to
a ci
r
cle a
r
e al
w
a
ys
c
on
g
ru
e
nt
to
each
ot
he
r
.
Seca
nt
A li
n
e
t
ha
t
i
nt
e
rs
ec
ts
a ci
r
cle a
t
two
po
i
nts
,
p
a
ss
i
n
g
t
h
rou
gh
t
he i
nt
e
r
i
or
.
C
omp
a
r
i
son
summ
a
ry
:
Li
n
e
typ
e P
o
i
nts
o
f i
nt
e
rs
ec
t
i
on
Pa
ss
e
s
t
h
rou
gh i
nt
e
r
i
or
?
Ta
n
ge
nt 1
N
o
(
tou
che
s
on
l
y
)
Seca
nt 2
Ye
s
Ch
or
d
(
a
s
a
s
eg
m
e
nt
)
2
(
e
n
d
po
i
nts
)
Ye
s
,
i
t
IS
t
he i
nt
e
r
i
or
p
iece
A ch
or
d i
s
r
eall
y
j
ust
t
he
"
i
ns
ide
p
iece
"
o
f
w
ha
t
wou
ld be a
s
eca
nt
li
n
e
—
t
he
s
eca
nt
i
s
t
he f
u
ll
i
nfin
i
t
e li
n
e
,
t
he ch
or
d i
s
t
he
fin
i
t
e
s
eg
m
e
nt
be
tw
ee
n
t
he
two
ci
r
cle
po
i
nts
.
2
.
ANGLES
—
Dee
p
Di
v
e
Ce
ntr
al A
n
gle
Ve
rt
e
x
i
s
a
t
t
he CENTER
;
t
he
two
s
ide
s
a
r
e
r
adii g
o
i
n
g
out
to
t
he ci
r
cle
.
R
u
le
:
The ce
ntr
al a
n
gle
'
s
deg
r
ee
m
ea
sur
e i
s
de
fin
ed
to
be EQUAL
to
t
he a
r
c i
t
c
uts
off
.
m
∠
ce
ntr
al
=
m
(
i
nt
e
r
ce
pt
ed a
r
c
)
Thi
s
i
s
e
ss
e
nt
iall
y
t
he de
fin
i
t
i
on
t
ha
t
le
ts
us
m
ea
sur
e a
r
c
s
i
n
deg
r
ee
s
a
t
all
—
a
r
c
s
a
n
d
t
hei
r
ce
ntr
al a
n
gle
s
a
r
e
num
e
r
icall
y
ide
nt
ical
.
I
ns
c
r
ibed A
n
gle
Ve
rt
e
x
i
s
ON
t
he ci
r
cle i
ts
elf
;
t
he
two
s
ide
s
a
r
e ch
or
d
s
str
e
t
chi
n
g
to
two
ot
he
r
po
i
nts
on
t
he
ci
r
cle
.
I
ns
c
r
ibed A
n
gle The
or
e
m
:
A
n
i
ns
c
r
ibed a
n
gle i
s
al
w
a
ys
HALF
o
f
t
he a
r
c i
t
i
nt
e
r
ce
pts
.
m
∠
i
ns
c
r
ibed
=
½
·
m
(
i
nt
e
r
ce
pt
ed a
r
c
)
Wh
y
t
hi
s
m
a
tt
e
rs
—
t
he
"
l
oo
k f
or
t
he a
r
c
"
tr
ick
:
t
he a
r
c a
n
i
ns
c
r
ibed a
n
gle i
nt
e
r
ce
pts
i
s
t
he
a
r
c
t
ha
t
d
o
e
s
NOT c
ont
ai
n
t
he
v
e
rt
e
x
—
t
he
"
fa
r
s
ide
"
a
r
c be
tw
ee
n
t
he
two
ot
he
r
po
i
nts
.
C
oro
lla
r
ie
s
(
t
hi
n
g
s
t
ha
t
f
o
ll
ow
f
rom
t
he
t
he
or
e
m
):
1
.
Sa
m
e a
r
c
→
s
a
m
e a
n
gle
.
If
two
di
ff
e
r
e
nt
i
ns
c
r
ibed a
n
gle
s
i
nt
e
r
ce
pt
t
he e
x
ac
t
s
a
m
e a
r
c
,
t
he
y
a
r
e c
on
g
ru
e
nt
to
each
ot
he
r
,
r
ega
r
dle
ss
o
f
w
he
r
e
t
hei
r
v
e
rt
ice
s
s
i
t
on
t
he ci
r
cle
.
2
.
A
n
gle i
ns
c
r
ibed i
n
a
s
e
m
ici
r
cle
=
90
°.
If
t
he i
nt
e
r
ce
pt
ed a
r
c i
s
a
s
e
m
ici
r
cle
(
180
°),
t
he
n
t
he i
ns
c
r
ibed a
n
gle
=
½
(
180
°)
=
90
°.
Thi
s
i
s
a
v
e
ry
c
ommon
"
hidde
n
r
igh
t
a
n
gle
"
tr
ick
—
if
you
s
ee a
tr
ia
n
gle i
ns
c
r
ibed i
n
a ci
r
cle
w
i
t
h
on
e
s
ide a
s
t
he dia
m
e
t
e
r
,
t
ha
t
tr
ia
n
gle ha
s
a
r
igh
t
a
n
gle
oppos
i
t
e
t
he dia
m
e
t
e
r
.
3
.
I
ns
c
r
ibed
qu
ad
r
ila
t
e
r
al
:
oppos
i
t
e a
n
gle
s
o
f a
qu
ad
r
ila
t
e
r
al i
ns
c
r
ibed i
n
a ci
r
cle add
up
to
180
°
(
supp
le
m
e
nt
a
ry
).
(
G
oo
d
to
k
now
,
t
h
ou
gh i
t
'
s
a
st
e
p
be
yon
d
t
he ba
s
e
c
urr
ic
u
l
um
—
m
e
nt
i
on
ed f
or
c
omp
le
t
e
n
e
ss
.)
Ce
ntr
al
vs
.
I
ns
c
r
ibed
—
s
ide
-
b
y
-
s
ide
Ce
ntr
al A
n
gle I
ns
c
r
ibed A
n
gle
Ve
rt
e
x
l
o
ca
t
i
on
Ce
nt
e
r
O
n
t
he ci
r
cle
Side
s
m
ade
o
f
2
r
adii
2
ch
or
d
s
Rela
t
i
ons
hi
p
to
a
r
c E
qu
al
to
a
r
c Half
o
f a
r
c
3
.
ARCS
—
Dee
p
Di
v
e
A
r
c Mea
sur
e
(
deg
r
ee
s
)
Mi
nor
a
r
c
:
t
he
s
h
ort
e
r
p
a
t
h be
tw
ee
n
two
po
i
nts
,
al
w
a
ys
<
180
°.
Na
m
ed
w
i
t
h
2
le
tt
e
rs
,
e
.
g
.
a
r
c AB
(
t
he
s
h
ort
e
r
w
a
y
a
roun
d
).
Maj
or
a
r
c
:
t
he l
on
ge
r
p
a
t
h be
tw
ee
n
t
he
s
a
m
e
two
po
i
nts
,
al
w
a
ys
>
180
°.
Na
m
ed
w
i
t
h
3
le
tt
e
rs
to
a
vo
id a
m
big
u
i
ty
,
e
.
g
.
a
r
c ACB
(
g
o
e
s
t
h
rou
gh
po
i
nt
C
to
di
st
i
n
g
u
i
s
h i
t
f
rom
t
he
m
i
nor
a
r
c
).
Se
m
ici
r
cle
:
e
x
ac
t
l
y
half
t
he ci
r
cle
,
180
°.
F
orm
ed
w
he
n
t
he
two
e
n
d
po
i
nts
a
r
e
c
onn
ec
t
ed b
y
a dia
m
e
t
e
r
.
Rela
t
i
ons
hi
p
be
tw
ee
n
m
i
nor
a
n
d
m
aj
or
a
r
c f
or
t
he
s
a
m
e
two
po
i
nts
:
m
(
m
i
nor
a
r
c
)
+
m
(
m
aj
or
a
r
c
)
=
360
°
A
r
c Addi
t
i
on
P
ostu
la
t
e
:
If
po
i
nt
B lie
s
on
a
r
c AC
(
be
tw
ee
n
A a
n
d C
),
t
he
n
:
m
(
a
r
c AB
)
+
m
(
a
r
c BC
)
=
m
(
a
r
c AC
)
Thi
s
wor
k
s
j
ust
like
t
he Seg
m
e
nt
Addi
t
i
on
P
ostu
la
t
e
,
b
ut
f
or
a
r
c
s
i
nst
ead
o
f
str
aigh
t
li
n
e
s
.
A
r
c Le
n
g
t
h
(
a di
st
a
n
ce
,
not
deg
r
ee
s
)
A
r
c le
n
g
t
h i
s
a PORTION
o
f
t
he ci
r
cle
'
s
tot
al ci
r
c
um
fe
r
e
n
ce
(
C
=
2
π
r
),
m
a
t
chi
n
g
w
ha
t
e
v
e
r
f
r
ac
t
i
on
o
f
360
°
t
he a
r
c
r
e
pr
e
s
e
nts
.
F
ormu
la
:
A
r
c le
n
g
t
h
=
(
a
r
c
m
ea
sur
e
/
360
°)
×
2
π
r
S
t
e
p
-
b
y
-
st
e
p
pro
ce
ss
:
1
.
Fi
n
d
w
ha
t
f
r
ac
t
i
on
o
f
t
he f
u
ll ci
r
cle
t
he a
r
c
r
e
pr
e
s
e
nts
:
(
a
r
c
m
ea
sur
e
)/
360
2
.
Fi
n
d
t
he ci
r
cle
'
s
tot
al ci
r
c
um
fe
r
e
n
ce
:
2
π
r
(
or
π
d
)
End of Document
328
