LESSON 11.2 CHORDS AND ARCS

OBJECTIVE: To use chords, arcs and central angles to solve problems

To recognize properties of lines through the center of a circle

Label each picture as a chord, arc or a central angle:

x

arc chordcentral angle

Theorem 11.4

Within one circle or within (two or more) congruent circles:

arcs have central angles

central angles have chords

chords have arcs

(1)

(2)

(3)

IFS AND THENS

Example #1: In the diagram, circle O circle D. Given that BC PF, what can you conclude? And why (theorem)?

O D

AND

BC PF

C

B

O

P

D F

Theorem:

arcs have ’s

Theorem:

’s have chords

they are equidistant from the center.

they are .center of a circle, then

Theorem 11.5

Within one circle or within (2 or more congruent circles): (Biconditional)

If chords are equidistant from the(1)

(2) If two or more chords are , then

C

AB

DE

F

G

IF THEN AB CD

AB CD EG FG

EG FG

IF THEN

Ex. #2 Find a. Give reason (theorem).

Therefore, a =

So, they are

If chords are equidistant from the center of the Circle, then they are .

25 un.

THEOREM

a and PR are equidistant from center.

Theorem 11.6In a circle, if a diameter is perpendicular to a chord, then it

bisects the chord and its arcs.

IF THEN

Theorem 11.7

In a circle, if a diameter bisects a chord (that is not another diameter) then it is

perpendicular to the chord.

IF THEN

Theorem 11.8

In a circle, if a segment is the perpendicular bisector of a chord, then

it contains the center of a circle

IF

A

B

THEN

AB passes through the center of the circle.

A

B

Ex. #3 Find r. State the reason (theorem).

If KN were extended, itwould be a diameter and it is to LM.

Therefore,

r2 = 72 + 32 r2 = 49 + 9 r2 = 58 r = 58

If a diameter is to a chord then it bisectsthe chord.

it bisects LM.So, LN = 7. Why?

Ex. #4 Find y. State the reason (theorem)

Is this a right triangle?

Yes.

152 = y2 + 112 225 = y2 + 121 104 = y2

2 26 = y

If a diameter bisects a chord then it is to the chord.

Why?

ASSIGNMENT: Page 593 #1 – 16

Write out the theorem used for #3-16