CIRCLES and the POINTS, SEGMENTS, LINES RELATED TO IT
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Transcript of CIRCLES and the POINTS, SEGMENTS, LINES RELATED TO IT
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THE CIRCLE and the
Geometric Figures Related
to ItPoints
Segments
Lines
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PICTURE! PICTURE!
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Bangui Windmills
by Agnes Manalofrom Google Images
G
O
D
•
•
•
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LEO The Lionby stylecraze
from Google Images
V
L
E
S
O
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Ziplinefrom Google Images
Y
u
O
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DEFINITION
A
Note: A circle is named by its center. The circle above is named circle A or .
A circle is the set of all points in a plane that are the same distance from a given point, called the center of a circle.
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Using circle A,1. Draw the following points:a. L inside circle A; b. G outside circle A; c. N, I, C, and E on circle A.
LET’S EXPLORE!
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POINTS
A
L
Interior points
A
G
AI
E
Exterior points
Points on the circle
C
N
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Using circle A,2. Connect the following points:
a. A and I; b. C and N; c. E and C.
LET’S EXPLORE!
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SEGMENTS
A
I
diameterchordradiusC
ANA
E
C
A of
radius a is AI
A of
chord a is NC
A of
diameter a is EC
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RadiusLine segment whose endpoints are the center of a circle and any point on the circle
Definition:
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Chord
Line segment whose endpoints are any two points on a circle
Definition:
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DiameterLine segment that passesthrough the center of a circle, and whose endpoints lie on the circle
Definition:
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3. Compare the measures of the segments AI, AE and AC.4. How is the measure of segment EC related to themeasures of segments AI, AE, and AC?
LET’S EXPLORE!
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SEGMENTS
A
I
diameterchordradiusC
ANA
E
C
A of
radius a is AI
A of
chord a is NC
A of
diameter a is EC
Note: All radii of the same circle are congruent.The diameter is twice the radius.The diameter is the longest chord in a circle.
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Using circle A,3. Draw a line containing the points:
a. E and G; b. I and C;
LET’S EXPLORE!
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LINES
G
E
secanttangentC
I
A of
secant a is IC
A of
tangenta is EG
AA
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Tangent• A line is tangent to
the circle if it touches it just once. Such a line is called a tangent or a tangent line. The point where the tangent touches the circle is called the point of tangency.
• We can also speak of tangent segments or rays.
Definition:
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Secant• A line that intersects
the circle twice is called a secant line or a secant.
• Line segments and rays may also be secants.
• Often, secants are drawn from a point outside of the circle to a point on the circle.
Definition:
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Identify each of the following as related to ʘ A.1. A2. RP3. PI4. SR5. IS6. PE7. AR8. SI9. AS10. P
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Name each of the following:
1. a circle 2. one interior point3. four exterior points4. four points on the circle 5. center 6. two points of tangency 7. four radii8. a chord9. two diameters10. two tangents11. a secant
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Work in pairs and try this!Using the circle at the right, A. Draw: (1) radius HJ; (2) diameter IC; (3) chord IS; (4) a line passing through points H and R; (5) line ST
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Work in pairs and try this!Using the circle at the right, B. Connect the points: (6) T and C; (7) C and H (8) H and I
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Work in pairs and try this!
Using the circle at the right, C. Name the following: (9) a circle; (10) an exterior point (11) a tangent line (12) a secant line (13) a point of tangency (14 - 16) three radii (17 - 20) four chords (aside from IS or SI)
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Answers:
S
CJ
I
H R
T
9. J10. R11. HR or RH12. TS or ST13. H14 -16. HJ or JH IJ or JI CJ or JC17 - 20
HI or IHCT or TCCH or HCST or TS
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SEGMENTS
A
I
diameterchordradiusC
ANA
E
C
A of
radius a is AI
A of
chord a is NC
A of
diameter a is EC
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LINES
G
E
secanttangentC
I
A of
secant a is IC
A of
tangenta is EG
AA
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THE CIRCLE and the
Geometric Figures Related
to ItPoints
Segments Lines
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THE CIRCLE and the
Geometric Figures Related
to ItPoints
Segments
![Page 31: CIRCLES and the POINTS, SEGMENTS, LINES RELATED TO IT](https://reader034.fdocuments.in/reader034/viewer/2022051400/54bbaee14a79598c4d8b45bf/html5/thumbnails/31.jpg)
THE CIRCLE and the
Geometric Figures Related
to ItPoints