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An Affirmation
Please read the following and consider
yourself in it.
I am capable of learning. I can
accomplish mathematical tasks.
I am ultimately responsible for
my learning.
GSE Geometry: Arc,
Angles, and Area.
Objectives
SWBAT understand that ALL circles are similar IOT find
circumference and areas of circles
SWBAT apply the relationship between central, inscribed, and
circumscribed angles IOT solve for unknown quantities in a circle.
SWBAT apply relationships among inscribed angles, radii, chords,
tangents and secants IOT solve for unknown quantities in a circle.
SWBAT define radian measure and derive the formula for area of a
sector IOT solve circle problems.
Chord Properties and
Segments Lengths in
Circles
If two chords are
congruent, then their
corresponding arcs are
congruent.
1.Solve for x.
8x – 7
8x – 7 = 3x + 3
x=2
3x + 3
2.Find the length of WX.
y  4  2y  3
4y3
y 7
WX  11cm
3. Find mAB
360 – 100
260 divided by 2
130º
If two chords are
congruent, then they
are equidistant from the
center.
4. In K, K is the midpoint of RE. If TY = -3x
+ 56 and US = 4x, find the length of TY.
3 x  56  4 x
56  7x
U
T
K
E
x=8
R
S
Y
TY = 32
If a diameter is perpendicular to a
chord, then it also bisects the chord.
This results in congruent arcs too.
Sometimes, this creates a right triangle
& you’ll use Pythagorean Theorem.
5. IN Q, KL  LZ. If CK = 2x + 3
and CZ = 4x, find x.
2x  3  4x
Q
Z
C
L
K
x = 1.5
6. In P, if PM  AT, PT = 10, and
PM = 8, find AT.
8   MT   10
2
2
2
64   MT   100
2
 MT   36
2
P
A
M8
10
T
MT = 6
AT = 12
7. Find the length of CE
BD is a radius.
CB is a radius.
What is the
length of the
radius?
25
2
2
20  x  25
x  15
Now double it to
find CE.
25
x
2
30
8.Find the length of LN.
MK and KL are radii.
2
2
14  x  50
2
x  48
x
50
Now double it to
find LN.
LN = 96
Segment
Lengths in
Circles
part   part  = part   part 
Go down the chord and multiply
9. Solve for x.
9  2  6x
18  6x
x=3
9
x
6
2
10. Find the length of DB.
12  8  3 x  2 x
2
96  6x
A
12
D
2x
3x
B
8
C
16  x
2
x=4
DB = 20
11. Find the length of AC and DB.
A
x
5 x  10  x  4 
D
x–4
5
10
B
C
5 x  10 x  40
5 x  40
x= 8
AC = 13
DB = 14
outside whole  outside whole
Sometimes you have to add to get the whole.
12. Solve for x.
x = 31
20
7
4
x
7(20) = 4 (4 + x)
140 = 16 + 4x
124 = 4x
13. Solve for x.
x
x = 11.8
5
8
6
6(6 + 8) = 5 (5 + x)
84 = 25 + 5x
59 = 5x
14. Solve for x.
(x – 6)(x + 16) = 0
x=6
10
x
4
x(x + 10) = 8(8 + 4)
2
x +10x = 96
x2 +10x – 96 = 0
8
tan = outside   whole 
2
15.Solve for x.
12
x
24
242 =12(12 + x)
576 = 144 + 12x
432 = 12x
x = 36
16.Solve for x.
5
15
x
x = 10
x2 = 5 (5 + 15)
x2 = 100