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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