Chapter 6:Chapter 6:Properties of CirclesProperties of Circles

Objective:Objective: Learn relationships among chords, arcs, Learn relationships among chords, arcs,

and anglesand angles Discover properties of tangent linesDiscover properties of tangent lines Learn how to calculate the length of an Learn how to calculate the length of an

arcarc

Circle terms we know:Match the terms to the examples

9. Semicircle

8. Major Arc

7. Minor Arc

6. Tangent

5. Diameter

4. Chord

3. Radius

2. Concentric Circles

1. Congruent Circles

Terms DC A.

TG B.

AB D.

OE C.

E.

F.G. RQ

H. PRQ

I. PQR

Chord PropertiesChord Properties

Objective:Objective:

Discover properties of chordsDiscover properties of chords

     AOB,   BOC,   COD,   DOA, and   DOB are central angles of circle O.

  PQR,   PQS,   RST,   QST, and    QSR are not central angles of circle P.

Central Angle

A central angle has it vertex at the center of the circle

Inscribed Angle

  ABC,   BCD, and   CDE areinscribed angles.

  PQR,   STU, and   VWX are not inscribed angles.

An inscribed angle has its vertex on the circle and its sides are chords.

1. Construct large circle O

2. Construct to congruent chords and label AB and CD

3. Measure and compare angles the central angles of arcs AB & CD

Chord Central Angles ConjectureIf two chords in a circle are congruent, then they determine two central angles that are ____________.

Chord Arcs ConjectureIf two chords in a circle are congruent, then their intercepted arcs are congruent.

congruent

O

D

C

B

A

1. Construct the perpendicular for O to AB and O to CD.Label intersection M and N.

2. Measure AM, BM, CN, DN

3. Measure ON and OM

O

D

C

B

A

Perpendicular to a Chord ConjectureThe perpendicular from the center of a circle to a chord is the ___________ of the chord.bisector

Chord distance to Center ConjectureTwo congruent chords in a circle are ___________ from the center of the circle.

equidistant

Perpendicular bisector of a Chord ConjectureThe perpendicular bisector of a chord passes through the _______ of the circle.center

Pg 310 #1-12, 16, 19-22

N

M

Perpendicular to a Chord ConjectureThe perpendicular from the center of a circle to a chord is the ___________ of the chord.

Chord distance to Center ConjectureTwo congruent chords in a circle are ___________ from the center of the circle.

Perpendicular bisector of a Chord ConjectureThe perpendicular bisector of a chord passes through the _______ of the circle.

bisector

equidistant

center