Transcript Lesson 1 Contents - Headlee's Math Mansion

5-Minute Check on Lesson 10-2
Transparency 10-3
In ⊙O, BD is a diameter and mAOD =55°. Find each measure.
1. mCOB
114°
2. mDOC
66°
3. mAOB
125°
Refer to ⊙P. Find each measure.
4. mLM
150°
5. mMOL
210°
6. Standardized Test Practice: If the measure of an arc is 68°,
what is the measure of its central angle?
A
34°
B
68°
C
102°
D
136°
Click the mouse button or press the
Space Bar to display the answers.
Lesson 10-3
Arcs and Chords
Objectives
• Recognize and use relationships between arcs
and chords
• Recognize and use relationships between arcs
and diameters
Vocabulary
• Inscribed Polygon – all vertices lie on the
circle
• Circumscribed – circle contains all vertices
of a polygon
TESSELLATIONS The rotations of a tessellation can
create twelve congruent central angles. Determine
whether
.
Because all of the twelve central
angles are congruent, the measure
of each angle is 360  12 or 30
Let the center of the circle be A.
The measure of PAQ is 5 • 30 or
150. Then
.
The measure of SAT is 5 • 30 or
150. Then
.
Answer: Since the measures of
equal,
.
are
ADVERTISING A logo for an advertising campaign is a
pentagon that has five congruent central angles.
Determine whether
.
Answer: no
Circle W has a radius of 10 centimeters. Radius
is
perpendicular to chord
which is 16 centimeters
long.
If
find
Since radius
to chord
Answer: 127
is perpendicular
Circle W has a radius of 10 centimeters. Radius
is
perpendicular to chord
which is 16 centimeters
long. Find JL.
Draw radius

A radius perpendicular
to a chord bisects it.
Definition of
segment bisector
Use the Pythagorean Theorem to find WJ.
Pythagorean Theorem
Simplify.
Subtract 64 from each side.
Take the square root of
each side.
Segment addition
Subtract 6 from each side.
Answer: 4
Circle O has a radius of 25 units. Radius
is
perpendicular to chord
which is 40 units long.
a. If
Answer: 145
b. Find CH.
Answer: 10
Chords
and
If the radius of
are equidistant from the center.
is 15 and EF = 24, find PR and RH.
are equidistant from P,
so
.
Draw
to form a right triangle. Use the Pythagorean
Theorem.
Pythagorean Theorem
Simplify.
Subtract 144 from each side.
Take the square root of
each side.
Answer:
Chords
and
are equidistant from the center of
If TX is 39 and XY is 15, find WZ and UV.
Answer:
Summary & Homework
• Summary:
– The endpoints of a chord are also the endpoints
of an arc
– Diameters perpendicular to chords bisect chords
and intercepted arcs
• Homework:
– pg 540-543; 11-18; 30-33, 52