11 1 circles lesson

Parts of a Circle Parts of a Circle

You will learn to identify and use parts of circles.

1) circle2) center3) radius4) chord5) diameter6) concentric


A circle is a special type of geometric figure.

All points on a circle are the same distance from a ___________.center point

OB

A

The measure of OA and OB are the same; that is, OA OB


Definitionof a

Circle

A circle is the set of all points in a plane that are a givendistance from a given _____ in the plane, called the ______ of the circle.

point

center

P

Note: a circle is named by its center. The circle above is named circle P.


There are three kinds of segments related to circles.

A ______ is a segment whose endpoints are the center of the circle and apoint on the circle.

radius

A _____ is a segment whose endpoints are on the circle.chord

A ________ is a chord that contains the centerdiameter


Segmentsof

Circles

K

A

diameterchordradius

R

KJ

K

T

G

KA is a radius of K

JR is a chord of K

GT is a diameter of K

From the figures, you can not that the diameter is a special type of _____that passes through the center.

chord


C

A

D

B

Q

AD is a diam eter of Q .

Use Q to determine whether each statement is true or false.

False;

Segment AD does not go through the center Q.

AC is a chord of Q .

True;

AD is a radius of Q .

False;

Theorem11-1

Theorem11-2


All radii of a circle are _________.congruent

P

R

ST

G

PR≃ PG ≃ PS ≃ PT

The measure of the diameter d of a circle is twice themeasure of the radius r of the circle.

d = 2r or12

d= r


C

A

B

Q

3x-5

17

Find the value of x in Q.

3x – 5 = 2(17)

3x – 5 = 34

3x = 39

x = 13


If QR = 1, find RT

RT = TQ – QR RP Q T BA

P has a radius of 5 units, and T has a radius of 3 units.

RT = 3 – 1

RT = 2

If QR = 1, find PQ

PQ = PR – QR

PQ = 5 – 1

PQ = 4

If QR = 1, find AB

AB = 2(AP) + 2(BT) – 1

AB = 2(5) + 2(3) – 1

AB = 10 + 6 – 1

AB = 15


If AR = 2x, find AP in terms of x.

AR = 2(AP)RP Q T BA

P has a radius of 5 units, and T has a radius of 3 units.

2x = 2(AP)

x = AP

If TB = 2x, find QB in terms of x.

QB = 2(TB)

QB = 2(2x)

QB = 4x

S


Because all circles have the same shape, any two circles are similar.

However, two circles are congruent if and only if (iff) their radii are _________.congruent

Two circles are concentric if they meet the following three requirements:

Circle R with radius RT and circle R with radius RS areconcentric circles.

They lie in the same plane.

They have the same center.

They have radii of different lengths.R

T

11 1 circles lesson

Spiritual

Transcript of 11 1 circles lesson