10.1 lines and segments that intersect circles with answers
TRANSCRIPT
10.1 Lines and Segments that Intersect Circles with answersChapter
10 Circles 10.1 Lines That
Intersect Circles
line that intersects a circle at two points.
a line that intersects the circle at exactly one point.
– segment that has it’s endpoints on the circle.
a chord that contains the center of the circle.
– segment that has one endpoint at the center of the circle and the other endpoint on the circle.
Segments of a Circle
E
A
G
Radius
Diameter
Chord
Tangent
Secant
Center the point in the middle of the circle. Midpoint of the diameter and endpoint of a radius in the circle.
Drag the word to the correct location on the diagram. Center
the exact point is called the point of tangencypoint of tangency
Center Radius
1
2
3
4
5
1
2
3
4
5
diameter
chord
tangent
radius
secant
P
T
S
Is ST tangent to P?
In the diagram, point P is a point of tangency. Find the radius r of O.
O
QP
r
r
36
24
50 ft
Hint: check answers by moving circles.
Use your knowledge about tangents to solve for EF and QS.
10.1 Lines and Segments that Intersect Circles with answers
Properties of Radii and Chords
2. If a diameter is 50 units long and a chord is 30 units long, find the distance between the 2 segments.
1. Find CD.
C
A
B
Justin's bike has wheels with a 27 in. diameter.
a. What are AC and AD if DB is 7 in.? 13.5 in. 6.5 in. b. What is CD to the nearest tenth of an inch? 11.8 in. c. What is CE, the length of the top of the bike stand? 23.7 in.
Warm up DAY TWO 10.1
10.1 Lines and Segments that Intersect Circles with answers
Wikki Stick Intro Activity
Ch. 10 Circles: 10.1 Lines that intersect Circles
Grab wiki sticks bag and the communicators. Follow the directions and
answer the questions in your notes.
10.1 Lines and Segments that Intersect Circles with answers
HW for 10.1
pg. 534: 5 9(o), 19 25 (o), 29 33 (o), 49, 50
Attachments
Circle Intro Activity with WIKKI STICKS 2012.docx
Circle Intro Activity
1. Create a DIAMETER of the circle using a blue string.
2. Create a RADIUS of the circle using a yellow string.
3. Create a SECANT of the circle using an orange string.
4. Create a TANGENT of the circle using a green string that touches the RADIUS. Is the TANGENT parallel, perpendicular, or neither to the RADIUS?
5. Using purple strings, create TWO CHORDS of the circle, so that the DIAMETER and BOTH CHORDS make a triangle. Is the triangle acute, right, or obtuse?
6. What is the circumference of your circle? (Use a ruler to get the diameter.)
7. What is the area of your circle?
8. What is the area of the part of the circle that lies above the DIAMETER? What is the area of the part that lies below the DIAMETER?
SMART Notebook
Circle Intro Activity using Wikki sticks, ruler, and protractor.
1. Create a DIAMETER of the circle using a blue string. How many times does the diameter fit around the circle’s edge?
2. Create a RADIUS of the circle using a yellow string. What is the relationship between this and the diameter?
3. Create a SECANT of the circle using an orange string. How does this differ from the diameter and radius?
4. Create a TANGENT of the circle using a green string that touches the RADIUS. Is the TANGENT parallel, perpendicular, or neither to the RADIUS?
5. Using purple and pink strings create TWO CHORDS of the circle, so that the DIAMETER and BOTH CHORDS make a triangle. Is the triangle acute, right, or obtuse? What is the longest chord in a circle?
6. What is the circumference of your circle?
7. What is the area of your circle? What is the ratio of the area above the diameter to the area whole circle?
8. A central angle is formed by two radii. Use the marker to draw an example of this angle on your circle then find the measure of the central angle in degrees using your protractor. What percentage of the circle does this angle represent?
Circle Intro Activity using Wikki sticks, ruler, and protractor.
1. Create a DIAMETER of the circle using a blue string. How many times does the diameter fit around the circle’s edge?
2. Create a RADIUS of the circle using a yellow string. What is the relationship between this and the diameter?
3. Create a SECANT of the circle using an orange string. How does this differ from the diameter and radius?
4. Create a TANGENT of the circle using a green string that touches the RADIUS. Is the TANGENT parallel, perpendicular, or neither to the RADIUS?
5. Using purple and pink strings create TWO CHORDS of the circle, so that the DIAMETER and BOTH CHORDS make a triangle. Is the triangle acute, right, or obtuse? What is the longest chord in a circle?
6. What is the circumference of your circle?
7. What is the area of your circle? What is the ratio of the area above the diameter to the area whole circle?
8. A central angle is formed by two radii. Use the marker to draw an example of this angle on your circle then find the measure of the central angle in degrees using your protractor. What percentage of the circle does this angle represent?
SMART Notebook
Attachments Page 1
Intersect Circles
line that intersects a circle at two points.
a line that intersects the circle at exactly one point.
– segment that has it’s endpoints on the circle.
a chord that contains the center of the circle.
– segment that has one endpoint at the center of the circle and the other endpoint on the circle.
Segments of a Circle
E
A
G
Radius
Diameter
Chord
Tangent
Secant
Center the point in the middle of the circle. Midpoint of the diameter and endpoint of a radius in the circle.
Drag the word to the correct location on the diagram. Center
the exact point is called the point of tangencypoint of tangency
Center Radius
1
2
3
4
5
1
2
3
4
5
diameter
chord
tangent
radius
secant
P
T
S
Is ST tangent to P?
In the diagram, point P is a point of tangency. Find the radius r of O.
O
QP
r
r
36
24
50 ft
Hint: check answers by moving circles.
Use your knowledge about tangents to solve for EF and QS.
10.1 Lines and Segments that Intersect Circles with answers
Properties of Radii and Chords
2. If a diameter is 50 units long and a chord is 30 units long, find the distance between the 2 segments.
1. Find CD.
C
A
B
Justin's bike has wheels with a 27 in. diameter.
a. What are AC and AD if DB is 7 in.? 13.5 in. 6.5 in. b. What is CD to the nearest tenth of an inch? 11.8 in. c. What is CE, the length of the top of the bike stand? 23.7 in.
Warm up DAY TWO 10.1
10.1 Lines and Segments that Intersect Circles with answers
Wikki Stick Intro Activity
Ch. 10 Circles: 10.1 Lines that intersect Circles
Grab wiki sticks bag and the communicators. Follow the directions and
answer the questions in your notes.
10.1 Lines and Segments that Intersect Circles with answers
HW for 10.1
pg. 534: 5 9(o), 19 25 (o), 29 33 (o), 49, 50
Attachments
Circle Intro Activity with WIKKI STICKS 2012.docx
Circle Intro Activity
1. Create a DIAMETER of the circle using a blue string.
2. Create a RADIUS of the circle using a yellow string.
3. Create a SECANT of the circle using an orange string.
4. Create a TANGENT of the circle using a green string that touches the RADIUS. Is the TANGENT parallel, perpendicular, or neither to the RADIUS?
5. Using purple strings, create TWO CHORDS of the circle, so that the DIAMETER and BOTH CHORDS make a triangle. Is the triangle acute, right, or obtuse?
6. What is the circumference of your circle? (Use a ruler to get the diameter.)
7. What is the area of your circle?
8. What is the area of the part of the circle that lies above the DIAMETER? What is the area of the part that lies below the DIAMETER?
SMART Notebook
Circle Intro Activity using Wikki sticks, ruler, and protractor.
1. Create a DIAMETER of the circle using a blue string. How many times does the diameter fit around the circle’s edge?
2. Create a RADIUS of the circle using a yellow string. What is the relationship between this and the diameter?
3. Create a SECANT of the circle using an orange string. How does this differ from the diameter and radius?
4. Create a TANGENT of the circle using a green string that touches the RADIUS. Is the TANGENT parallel, perpendicular, or neither to the RADIUS?
5. Using purple and pink strings create TWO CHORDS of the circle, so that the DIAMETER and BOTH CHORDS make a triangle. Is the triangle acute, right, or obtuse? What is the longest chord in a circle?
6. What is the circumference of your circle?
7. What is the area of your circle? What is the ratio of the area above the diameter to the area whole circle?
8. A central angle is formed by two radii. Use the marker to draw an example of this angle on your circle then find the measure of the central angle in degrees using your protractor. What percentage of the circle does this angle represent?
Circle Intro Activity using Wikki sticks, ruler, and protractor.
1. Create a DIAMETER of the circle using a blue string. How many times does the diameter fit around the circle’s edge?
2. Create a RADIUS of the circle using a yellow string. What is the relationship between this and the diameter?
3. Create a SECANT of the circle using an orange string. How does this differ from the diameter and radius?
4. Create a TANGENT of the circle using a green string that touches the RADIUS. Is the TANGENT parallel, perpendicular, or neither to the RADIUS?
5. Using purple and pink strings create TWO CHORDS of the circle, so that the DIAMETER and BOTH CHORDS make a triangle. Is the triangle acute, right, or obtuse? What is the longest chord in a circle?
6. What is the circumference of your circle?
7. What is the area of your circle? What is the ratio of the area above the diameter to the area whole circle?
8. A central angle is formed by two radii. Use the marker to draw an example of this angle on your circle then find the measure of the central angle in degrees using your protractor. What percentage of the circle does this angle represent?
SMART Notebook
Attachments Page 1