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You will learn to:

Recognize and use relationships between chords and diameters.

10-3 Objectives

Inscribed

Circumscribed

Vocabulary

Diameters and Chords

Diameters that are perpendicular to

chords create special segment and

arc relationships.

Theorem 10.3

In a circle: Graph Conclusion

If a radius (or diameter)

is perpendicular to a

chord, then it bisects

the chord and its arc.

The perpendicular

bisector of a chord is a

radius (or diameter).

Circle W has a radius of 10 centimeters.

Radius is perpendicular to chord

which is 16 centimeters long.

If find

Since radius is perpendicular to

chord

Answer: 127

Circle W has a radius of 10 centimeters.

Radius is perpendicular to chord

which is 16 centimeters long.

Find JL.

Draw radius

Use the Pythagorean Theorem to find WJ.

Answer: 4

Circle O has a radius of 25 units. Radius is

perpendicular to chord which is 40 units long.

a. If

b. Find CH.

Answer: 145

Answer: 10

OE2 = OH2 + EH2

252 = OH2 + 202

625 = OH2 + 400

OH2 = 225

OH = 15

OC = CH + HO

25 = CH + 15

CH = 25 - 15

CH = 10

Theorem 10.4

In a circle, or congruent

circle, two chords are

congruent if and only if

they are equal distance

from the center.

If PQ = PR then EF = GH

and

If EF = GH then PQ = PR

Chords and are equidistant from

the center. If the radius of is 15

and EF = 24, find PR and RH.

are equidistant from P,

so .

Draw to form a right triangle. Use the Pythagorean Theorem.

Answer:

Answer: UV = 72

Chords and are equidistant from the center of If TX is 39 and XY is 15, find WZ and UV.

Find NP.

Step 2 Use the Pythagorean Theorem.

Step 3 Find NP.

RN = 17 Radii of a are .

SN2 + RS2 = RN2

SN2 + 82 = 172

SN2 = 225

SN = 15

NP = 2(15) = 30

Substitute 8 for RS and 17 for RN.

Subtract 82 from both sides.

Take the square root of both sides.

RM NP , so RM bisects NP.

Step 1 Draw radius RN.

Using Radii and Chords

Find QR to the nearest tenth.

Step 2 Use the Pythagorean Theorem.

Step 3 Find QR.

PQ = 20 Radii of a are .

TQ2 + PT2 = PQ2

TQ2 + 102 = 202

TQ2 = 300

TQ 17.3

QR = 2(17.3) = 34.6

Substitute 10 for PT and 20 for PQ.

Subtract 102 from both sides.

Take the square root of both sides.

PS QR , so PS bisects QR.

Step 1 Draw radius PQ.

Your Turn

What did you learn today?

How to:

Recognize and use relationships between arcs and chords.

Assignment:

Page 540

11 – 35 odd, 44, 54, 58