find the area. chord properties and segments lengths in circles
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Find the Area
A lw
12A bh
. 271 2A ft . 226 95A mi
Chord Properties and
Segments Lengths in
Circles
If two chords are congruent, then their corresponding arcs are congruent.
8x – 7 3x + 3
8x – 7 = 3x + 3
1.Solve for x.
x = 2
2.Find the length of WX.
4 2 3y y 4 3y
7y11WX cm
3. FindmAB
130º
360 – 100 260 divided by 2
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.
Y
T
S
Kx = 8
U
RE
3 56 4x x 56 7x
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.
K
Q
C
L
Z x = 1.5
2 3 4x x
6. In P, if PM AT, PT = 10, and PM = 8, find AT.
T
AM
P
MT = 6AT = 12
22 28 10MT
264 100MT 2 36MT
108
7. Find the length of CE
30
2 2 220 25x 15x
BD is a radius.CB is a radius.What is the length of the radius?
25
x
Now double it to find CE.25
8.Find the length of LN.
LN = 96
2 2 214 50x
48xx 50
MK and KL are radii.
Now double it to find LN.
Segment Lengths
in Circles
partpart
partpart
part part = part part Go down the chord and multiply
9
2
6x
x = 3
9. Solve for x.9 2 6x
18 6x
10. Find the length of DB.
8
122x
3x x = 4
A
B
C
D
12 8 3 2x x 296 6x
216 x
DB = 20
11. Find the length of AC and DB.
x = 8
x5
x – 4
10
A
B
C
D 5 10 4x x 5 10 40x x 5 40x
AC = 13
DB = 14
outside whole outside wholeSometimes you have to add to get the
whole.
7
20
4
x
7(20) 4 (4 + x)
=
12. Solve for x.
140 = 16 + 4x124 =
4x
x = 31
8
5
6
x
6 (6 + 8)
5(5 + x)=
13. Solve for x.
84 = 25 + 5x59 = 5x
x = 11.8
4
x
8
10
x (x + 10)
8(8 + 4)=
14. Solve for x.
x2 +10x = 96x2 +10x – 96 =
0
x = 6(x – 6)(x + 16) =
0
2tan = outside whole
24
12 x
242
= 12
(12 + x)576 = 144 + 12x
x = 36
15.Solve for x.
432 = 12x
155
x
x2 = 5 (5 + 15)x2 = 100
x = 10
16.Solve for x.
Practice
Workbook Page 232
Homework
Worksheet
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