A

B

C

D

In the same circle, or in congruent circles, two minor arcs are congruent

if and only if their corresponding chords are congruent.

AB CD IFF AB = DC

120 120

12 in.

x

x = 12 in.

2x + 10 x + 40

2x + 10= x + 40

x = 30

A

B

C

D

What can you tell me about segment AC if you know it is the perpendicular bisectors of segments DB?

It’s the DIAMETER!!!

Ex. 1 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

y4

x

60x = 4

y = 30

Example 2EX 2: In P, if PM AT, PT = 10, and PM = 8, find AT.

T

AM

P

MT = 6AT = 12

Example 3In R, XY = 30, RX = 17, and RZ XY.

Find RZ.

R

X

Z

Y

RZ = 8

Example 4 IN Q, KL LZ. IF CK = 2X + 3 and CZ = 4x, find x.

K

Q

C

L

Zx = 1.5

In the same circle or in congruent circles, two chords are congruent if

and only if they are equidistant from the center.

A

B

C

D

M

L

P

AD BC

IFF

LP PM

Ex. 5: In A, PR = 2x + 5 and QR = 3x –27. Find x.

P

R

Q

A

x = 32

Ex. 6: IN K, K is the midpoint of RE. If TY = -3x + 56 and US = 4x, find x.

Y

T

S

K

x = 8

U

R

E