Chapter 10: CirclesChapter 10: Circles10.3.1 Apply Properties of Chords

Arcs and ChordsArcs and ChordsFor any circle (or congruent circles),

two arcs are congruent iff their corresponding chords are congruent◦Congruent Chord Congruent Arc (CCCA)

A

CB

E

D

AD BE

iff

AD BE

Chord Diameter Chord Diameter relationship relationship

A chord is a perpendicular bisector of another chord iff the perpendicular chord is a diameter◦ Chord Diameter Perpendicular Bisector Theorem

(CDP)◦ The diameter bisects the arc formed by the chord

A

CB

D

E

BD DE

F

iff

BF FE

BE ┴ (Diameter)

and

Chord Distance TheoremChord Distance TheoremTwo chords are congruent iff they

are equidistant from the center of the circle (or congruent circles)

A

C

B

ED

F

G

iff

iff

AD BE(how do we know?)

GC FC

AD BE

Find the value of x and y for each Find the value of x and y for each circlecircle

A

CB

D

E

F

AD = 180⁰BF = 13x – 2y FE = 20

BD = 20⁰ DE = 8.5x +yA

C

B

ED

F

G

Find the values of x and y so thatAD = BE

(x –

y)⁰

25⁰

3y - 5x

20213 yx205.8 yx

40217 yx40217 yx+

6030 x2x

202)2(13 yy26y3

25 yx xy 53yx 25

yy 2553302 y

15y2515x

40x

HomeworkHomeworkp. 667 1, 2, 3 – 35odd, 37