Circle segments and volume
This presentation is the property of its rightful owner.
Sponsored Links
1 / 34

Circle Segments and Volume PowerPoint PPT Presentation


  • 80 Views
  • Uploaded on
  • Presentation posted in: General

Circle Segments and Volume. Chords of Circles Theorem 1. In the same circle, or in congruent circles two minor arcs are congruent if and only if their corresponding chords are congruent. Chord Arcs Conjecture.

Download Presentation

Circle Segments and Volume

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Circle segments and volume

Circle Segments and Volume


Chords of circles theorem 1

Chords of Circles Theorem 1


Circle segments and volume

In the same circle, or in congruent circles two minor arcs are congruent if and only if their corresponding chords are congruent.


Chord arcs conjecture

Chord Arcs Conjecture

In the same circle, two minor arcs are congruent if and only if their corresponding chords are congruent.

IFF

G

and

IFF

and


Solve for x

Solve for x.

8x – 7

3x + 3

8x – 7 = 3x + 3

x = 2


Example

Example

Find WX.


Example1

Example

Find

130º


Chords of circles theorem 2

Chords of Circles Theorem 2


Circle segments and volume

If a diameter is perpendicular to a chord, then it also bisects the chord and its arc.This results in congruent arcs too.Sometimes, this creates a right triangle & you’ll use Pythagorean Theorem.


Perpendicular bisector of a chord conjecture

If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

Perpendicular Bisector of a Chord Conjecture

H


Circle segments and volume

IN Q, KL  LZ. If CK = 2x + 3 and CZ = 4x, find x.

x = 1.5

Q

C

Z

K

L


Circle segments and volume

In P, if PM  AT, PT = 10, and PM = 8, find AT.

P

A

M

MT = 6

T

AT = 12


Chords of circles theorem 3

Chords of Circles Theorem 3


Perpendicular bisector to a chord conjecture

If one chord is a perpendicular bisector of another chord, then the bisecting chord is a diameter .

Perpendicular Bisector to a Chord Conjecture

  • is a diameter of the circle.


Circle segments and volume

  • ,

If one chord is a perpendicular bisector of another chord, then the first chord is a diameter.


Chords of circles theorem 4

Chords of Circles Theorem 4


Circle segments and volume

In the same circle or in congruent circles two chords are congruent when they are equidistant from the center.


Chord distance to the center conjecture

Chord Distance to the Center Conjecture


In k k is the midpoint of re if ty 3x 56 and us 4x find the length of ty

In K, K is the midpoint of RE. If TY = -3x + 56 and US = 4x, find the length of TY.

U

T

K

E

x = 8

R

S

Y

TY = 32


Example2

Example

30

CE =


Example3

Example

LN =

96


Circle segments and volume

Segment Lengths in Circles


Circle segments and volume

Two chords intersect

INSIDE the circle

Type 1:

part

part

part

part

Go down the chord and multiply


Circle segments and volume

Solve for x.

9

6

x

2

x = 3


Find the length of db

12

2x

8

3x

Find the length of DB.

A

D

x = 4

C

DB = 20

B


Find the length of ac and db

Find the length of AC and DB.

D

A

x – 4

x

C

5

10

x = 8

AC = 13

DB = 14

B


Circle segments and volume

Two secants intersect

OUTSIDE the circle

Type 2:


Circle segments and volume

Ex: 3 Solve for x.

B

13

A

7

E

4

C

x

D

7

(7 + 13)

=

4

(4 + x)

x = 31

140 = 16 + 4x

124 = 4x


Circle segments and volume

Ex: 4 Solve for x.

B

x

A

5

D

8

6

C

E

6

(6 + 8)

=

5

(5 + x)

84 = 25 + 5x

x = 11.8

59 = 5x


Circle segments and volume

Ex: 5 Solve for x.

B

10

A

x

D

4

8

C

E

x

(x + 10)

=

(8 + 4)

8

x2+10x = 96

x = 6

x2 +10x – 96 = 0


Circle segments and volume

Type 2 (with a twist):

Secant and Tangent


Circle segments and volume

Ex: 5 Solve for x.

x

12

24

(12 + x)

242

=

12

x = 36

576 = 144 + 12x


Circle segments and volume

Ex: 6

5

15

x

(5 + 15)

x2

=

5

x2 = 100

x = 10


  • Login