NAME ______DATE______PERIOD ______
10-1 Study Guide and Intervention
Circles and Circumference
Chapter 105Glencoe Geometry
NAME ______DATE______PERIOD ______
Segments in CirclesAcircle consists of all points in a plane that are agiven distance, called the radius, from a given point called the center.A segment or line can intersect a circle in several ways.
• A segment with endpoints that are at the center and on thecircle is a radius.
• A segment with endpoints on the circle is a chord.
• A chord that passes through the circle’s center and made up ofcollinear radii is adiameter.
For a circle that has radius r and diameter d, the following are true
r = r = d = 2r
chord: ,
radius: , ,
diameter:
Chapter 105Glencoe Geometry
NAME ______DATE______PERIOD ______
Example
a. Name the circle.
The name of the circle is ⨀O.
b. Name radii of the circle.
, , , and are radii.
c. Name chords of the circle.
andare chords.
Exercises
For Exercises 1-7, refer to
1. Name the circle.
2. Name radii of the circle.
3. Name chords of the circle.
4. Name diameters of the circle.
5. If AB = 18 millimeters, find AR.
6. If RY = 10 inches, find AR and AB.
7. Is ≅? Explain.
10-1 Study Guide and Intervention(continued)
Circles and Circumference
Circumference The circumference of a circle is the distance around the circle.
Circumference / For a circumference of C units and a diameter of d units of a radius of r units,C = πd or C = 2πr
Example: Find the circumference of the circle tothe nearest hundredth.
C = 2πr Circumference formula
= 2π(13) r =13
= 26π Simplify.
≈ 81.68 Use a calculator.
The circumference is 26π or about 81.68 centimeters.
Exercises
Find the diameter and radius of a circle with the given circumference. Round tothe nearest hundredth.
1. C = 40 in. 2. C = 256 ft
3. C = 15.62 m 4. C = 9 cm
5. C = 79.5 yd6. C = 204.16 m
Find the exact circumference of each circle using the given inscribed orcircumscribed polygon.
7. 8.
9. 10.
11. 12.
10-2 Study Guide and Intervention
Measuring Angles and Arcs
Chapter 1011Glencoe Geometry
NAME ______DATE______PERIOD ______
Angles and Arcs Acentral angle is an anglewhose vertex is at the center of a circle and whosesides are radii. A central angle separates a circleinto two arcs, a major arc and a minor arc.
Here are some properties of central angles and arcs.
• The sum of the measures of the central angles ofa circle with no interior points in common is 360.
• The measure of a minor arc is less than 180 andequal to the measure of its central angle.
• The measure of a major arc is 360 minus themeasure of the minor arc.
• The measure of a semicircle is 180.
• Two minor arcs are congruent if and only if theircorresponding central angles are congruent.
• The measure of an arc formed by two adjacentarcs is the sum of the measures of the two arcs.(Arc Addition Postulate)
is a minor arc.
is a major arc.
∠GEF is a central angle.
m∠HEC+ m∠CEF+ m∠FEG+ m∠GEH= 360
m= m∠CEF
m= 360 – m
≅if and only if ∠CEF ≅∠FEG.
m+ m= m
Chapter 1011Glencoe Geometry
NAME ______DATE______PERIOD ______
Example:is a diameter of ⨀R. Find mand m.
∠ARB is a central angle and m∠ARB= 42, so m= 42.
Thus m= 360 – 42 or 318.
Exercises
Find the value of x.
1.2.
andare diameters of ⨀O. Identify each arc as a major arc, minor arc, orsemicircle of the circle.
Then find its measure.
3. m4. m
5. m6. m
7. m8. m
10-2 Study Guide and Intervention(continued)
Measuring Angles and Arcs
Arc Length An arc is part of a circle and its length is a part of the circumference ofthe circle.
The length of arc ℓ can be found using the following equation:
ℓ = ⋅ 2πr
Example: Find the length of . Round to the nearest hundredth.
The length of arc , can be found using the following equation: = · 2πr
= · 2πr Arc Length Equation
= · 2π(8) Substitution
≈ 18.85 in.Use a calculator.
Exercises
Use ⨀O to find the length of each arc. Round tothe nearest hundredth.
1. if the radius is 2 meters
2. if the diameter is 7 inches
3. ifBE = 24 feet
4. ifDO = 3 millimeters
Use ⨀P to find the length of each arc. Round tothe nearest hundredth.
5. , if MT = 7 yards
6. , if PR = 13 feet
7. , if MP = 2 inches
8. , if PS = 10 centimeters
Chapter 106Glencoe Geometry