Salient Features of India constitution especially power and functions
Circle and Its part
1.
2.
3. It has no width, depth, length, thickness -- no
dimension at all. It is named with a capital
letter: Point A; Point B; and so on.
4. It is a one-dimensional figure, which has
length but no width. A line is made of a set of
points which is extended in opposite
directions infinitely.
5. It is a straight
path of points
that has no
beginning or end.
It is a portion of a
line that has two
endpoints
It is a portion of a
line which has one
endpoint and
extends forever in
one direction.
8. It is described as a flat surface with infinite length
and width, but no thickness. It cannot be defined.
A plane is formed by three points. For every three
points in space, a unique plane exists.
9. Dinner plates and most coins
Pizza bases and rings
The letter after N
What shape are all these things?
10.
11. A circle is a shape with all points the same
distance from its center. A circle is named
by its center. Thus, the circle given is
called circle A since its center is at point A.
Some real world examples of a circle are a
wheel, a dinner plate and (the surface of)
a coin.
Circle and Its Part
What is Circle?
12. A Circle is Divided into 3 Parts
1. The points
INSIDE of
the circle
2. The points
OUTSIDE of
the circle
3. The
points ON
the circle
Note: The part of the plane which is inside the circle is known as the INTERIOR of
the circle, the plane which is the circle is known as the EXTERIOR of the
circle, and the part which is on the circle is known as ON the circle.
13.
14.
15. It is a line segment that passes through the center of the circle and
has its endpoints on the circle. All of them have the same length.
Example:
Therefore, AB is the
d_ _m_ _ _r of Circle O
16. It is a line segment that passes through the center of the circle and
has its endpoints on the circle. All of them have the same length.
Example:
Therefore, AB is the
diameter of Circle O
17. It is a line segment from the center of the circle to a point on
the circle. The plural is radii.
Example:
18. It is a line segment from the center of the circle to a point on
the circle. The plural is radii.
Example: In the diagram, O is the center of the
circle and OB is the radius of the circle.
The radii of a circle are all the same
length. The radius is half the length of
the diameter.
19. It is a line segment with both endpoints on the circle.
Example:
X
Y
20. It is a line segment with both endpoints on the circle.
Example:
The diameter is a special chord
that passes through the center of
the circle. The diameter would be
the longest chord in the circle.
Chord is XY
X
Y
21. A line that intersects the circle in two points
Example:
O
P
22. A line that intersects the circle in two points
Example:
A secant of a circle is a line that
intersects a circle at two distinct
points. Secant is derived from the
Latin word secare which means to
cut. It can also be understood as
the extension of the chord of a
circle that goes outside the circle.
Secant is OP
O
P
23. It is a line that touches a circle at only one point.
Example:
24. It is a line that touches a circle at only one point.
Example: A tangent is perpendicular to the radius at the
point of contact. The point of tangency is where a
tangent line touches the circle. In the above
diagram, the line containing the points B and C is a
tangent to the circle.
It touches the circle at point B and is perpendicular
to the radius OB Point B is called the point of
tangency. BC is perpendicular to OB
25. It is a half circle, formed by cutting a whole circle along a
diameter line, as shown below.
Example:
26. It is a half circle, formed by cutting a whole circle along a
diameter line, as shown below.
Example:
a semicircle is a one-
dimensional locus of points
that forms half of a circle. The
full arc of a semicircle always
measures 180° (equivalently, π
radians, or a half-turn). It has only
one line of symmetry (reflection
symmetry).
27. It is the shorter arc connecting
two endpoints on a circle . The
measure of this arc is less than
180°
Example:
28. It is the shorter arc connecting
two endpoints on a circle . The
measure of a minor arc is less
than 180°
A minor arc may refer to an
arc that is smaller than a
semicircle.
Example:
29. The longer arc connecting two
endpoints on a circle. The
measure of this arc is greater
than 180°
Example:
30. The longer arc connecting two
endpoints on a circle. The
measure of the major arc is
greater than 180°
A major arc is an arc larger
than a semicircle.
Example:
31. It is an angle whose apex
(vertex) is the center O of a circle
and whose legs (sides) are radii
intersecting the circle in two
distinct points A and B.
Example:
32. A central angle is an angle that forms
when two radii meet at the center of a
circle. Remember that a vertex is a point
where two lines meet to form an angle. A
central angle's vertex will always be the
center point of a circle.
Example:
33. An angle in a circle which is formed
by two chords that have a common
endpoint on the circle. This common
endpoint is the vertex of the angle.
Example:
34. In geometry, an inscribed angle is the angle
formed in the interior of a circle when two
chords intersect on the circle. It can also be
defined as the angle subtended at a point
on the circle by two given points on the
circle. Equivalently, an inscribed angle is
defined by two chords of the circle sharing
an endpoint.
Example:
35. It is a section of the circumference of a circle. It is encased on
either side by two different chords or line segments that meet at
one point, called a vertex, on the other side of the circle or in the
middle of the circle.
Example:
36. It is a section of the circumference of a circle. It is encased on either side by two
different chords or line segments that meet at one point, called a vertex, on the
other side of the circle or in the middle of the circle. The angle formed by these
two chords or line segments is called an inscribed angle or a central angle
depending on where the vertex lies.
Example:
37.
38. TEST 1.
1. Determine the following:
• the name of circle
• the radii
• the diameter
D
39. TEST 1.
1. Determine the following:
• the name of circle
Answer: Circle A
• the radii
Answer: AB or BA
AC or CA & AD or DA
• the diameter
Answer: CD or DC
D
40. TEST 2.
2. What is a line segment in
which both endpoints are on
the circle?
3. What is a line that intersects
the circle in two points?
4. What is a line that touches a
circle at only one point?
A
B
C
D
E
F
41. TEST 2.
2. What is a line segment in
which both endpoints are on
the circle?
ANSWER: CHORD / AB
3. What is a line that intersects
the circle in two points?
ANSWER: SECANT / CD
4. What is a line that touches a
circle at only one point?
ANSWER: TANGENT / EF
A
B
C
D
E
F
42. In the diagram above:
2. What angle is the central angle?
3. What angle is the inscribed angle?
1. A protractor is an
example of what
circle?
TEST III
43. In the diagram above:
2. What angle is the central angle?
ANSWER: ANGLE B
3. What angle is the inscribed angle?
ANSWER: ANGLE A
1. A protractor is an
example of what
circle?
ANSWER: SEMICIRCLE
TEST III