Find the Area. Chord Properties and Segments Lengths in Circles.

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