NAME:
SECTION
DATE
10Feb2025
E G P T
QUIZ (QT3) - Circle: Arc – Angle Summary /Area
Each blank is worth 1 point unless stated otherwise.
# = 84°, m CD
# = 38°, m DE
# =
Y
1) In the figure below, m BC
340
# = 60°, and AB and AF are tangents. Find
64°, m EF
Marc
Jan
Borra
each measure.
# = __________
114 0
a) m BF
g
O
1980
# = _________
i) m FBC
12 48
# = _________
c) m BFE
j) mÐ7 = __________
1318
d) mÐ5 = __________
k) mÐ1 = __________
490
m) mÐ4 = __________
1380
g) mÐ2 = __________
o) mÐ8 = __________
c) +Ð /
'
d) + -./
'
e) + -0/
11612002408
:
1388
38
&
W
1
49
68
3) Given the figure below, determine the following:
+Ð 123
+Ð 132
#
+ 12
(major arc)
300
1200
308
&
300
E
Goo
160o
1600
55555⃗ is tangent to the circle at
4) In the figure on the right, AF
# = 128°, mDE
# = 38°, and mCE
# = 104°, find:
B. If mBD
640
___________
b) mÐDBA
___________
c) mÐA
___________
d) mÐD
___________
e) mÐDCE
___________
100
Goo
↳
120/
a) mÐFBD
64
se
380
# = 128°,
2) In the figure below, if mÐP = 60° and m PSR
232
what is
64120
114
⑧
' = _________
f) m BDF
b)
+Ð .
7742
66
69
n) mÐ6 = __________
a) +Ð -
262
1180
O
2428
24
870
h) mÐ3 = __________
276
# = _________
b) m BFC
236
e) m '
FBD = _________
SCORE:
_______
-
900
1288
ego
is
e
148
F
5) A continuous belt runs around two wheels as
shown on the right. The wheels have radii 3 cm
and 15 cm and the distance between their
centers is 24 cm. Find the length of the belt.
=
15
I
15 cm
24
Ans:_____________
(2 pts.)
6) Refer to the figure on the right, find the exact value of the
following. Leave fractions in lowest terms.
a) If 78 = 4 and 8; = 10, find >?.
Ans:_______________
24
4
↳
Ans:_______________
b) If 2@ = 6, 8@ = 5, DEF @G = 3, find IJ.
c) If 2K = 3, K@ = 4, @G = 5 DEF KL = 12, find NO.
d) If QL = 9, Q7 = 15, DEF 78 = 6, find IS.
G
10
5
Ans:_______________
ziy
↑
15
Ans:_______________
I
e) If 7L = 7, LQ = 10, 78 = 5, find SI. Ans:_______________
7) The length of a rectangle is twice its width. A semicircle,
with the rectangle’s longer side as its diameter is drawn
tangent to the other longer side. If the width of the
rectangle is 3, find the area of the segment region (the region
on the upper part of the chord) .
-E
-
Ans: __________ ( 2 pts.)
8) Given the follwing regular polygons, find the indicated area
of each figure.
a) inside the square but outside the quarter circles.
3
M ( 2 pts.)
Ans: __________
c) inside the equilateral triangle but outside the circle.
d = 53 5
(
6
-
o
p
-55
=
12
-E
-
S
235-
75
Ans: __________ ( 2 pts.)
Y
=
5%. Y
55
=
25
.
28(
d) inside the circle but outside the regular
hexagon.
pi
100
↳ 25
V5
-
v=
255-
w
18
25
255
Ans: __________
( 2 pts.)
25
5
b) inside the equilateral triangle but outside the
three circular sectors.
7600
J
-
36
100-254
ulfam
100
9
24
1445- 21653
Ans: __________ ( 2 pts.)
1444
-
365
9) Find the area the middle region (sandwhich by the “yin”and
“yang”)
r= 15
10) Find the area of the region inside the square
but outside the four-petal region.
4
-
M 4
-
M
c
⑭
↑
-
E
&
44 4
-
4
10
-
S
32
87
Ans: __________
( 2 pts.)
-
754
Ans: __________ ( 2 pts.)