10-3 arcs and chords

10-3 Arcs and 10-3 Arcs and ChordsChords

Arcs and Chords

• In a circle (or 2 congruent circles) two minor arcs are congruent if and only if their corresponding chords are congruent.

A

B

C

D

CDABCDAB then If

Inscribed and Circumscribed Polygons

• If all the vertices of a polygon lie on a circle then the polygon is inscribed in the circle

• The circle is circumscribed about the polygon because it contains the vertices

A

B

C

D

E

Diameters and Chords

• If a diameter (or radius) is perpendicular to a chord then it bisects the chord and its arc

B

C

A

TU V

AVAT

UVUTTVBA

and

then , If

Example:

• Circle W has radius 10 cm. Radius WL is perpendicular to chord HK and HK is 16 cm.

• If mHL = 53, find mMK

• Find JL

HJ

K

L

W

M

Chords equidistant from the center• In a circle, 2 chords are congruent if and

only if they are equidistant from the center

• Example: EF and GH are equidistant form the center. If the radius is 15 and EF=24, Find PR and RH

R

P

QE

F

G

H

Example:• Radius of N is 18, NK=9, mDE=120

• Find m<HNE

• Find HN

• Find HE

• Find mGE

X

K

Y

N

D H E

G