4. 1. The word "circle" derives from the
Greek, kirkos "a circle," from the base ker-
which means to turn or bend.
2. Natural circles would have been
observed, such as the Moon, Sun.
3. In mathematics, the study of the circle
has helped inspire the development of
geometry, astronomy, and calculus.
5. A SET OF POINTS
WHICH ARE
EQUIDISTANT FROM A
FIXED POINT IS CALLED
CIRCLE.
6.
7.
8. An arc of a circle is any connected part of the
circle's circumference.
A sector is a region bounded by two radii and an
arc lying between
the radii.
A segment is a region bounded by a chord and an
arc lying between the chord's endpoints.
A line segment joining centre and any point on the
circle is called radius.
9.
10. Circle
Area = πr 2
Circumference=2πr
r = radius
11.
12. The circumference is the distance
around the outside of a circle.
A chord is a line segment whose
endpoints lie on the circle. A diameter
is the longest chord in a circle.
A tangent to a circle is a straight line
that touches the circle at a single
point.
A secant is a line passing through the
circle.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27. or
Sagitta
The sagitta is the vertical segment.
•The sagitta (also known as the versine) is a line segment drawn
perpendicular to a chord, between the midpoint of that chord and the
arc of the circle.
•Given the length y of a chord, and the length x of the sagitta,
the Pythagorean theorem can be used to calculate the radius of the
unique circle which will fit around the two lines:
Another proof of this result which relies only on two chord properties
given above is as follows. Given a chord of length y and with sagitta of
length x, since the sagitta intersects the midpoint of the chord, we know
it is part of a diameter of the circle. Since the diameter is twice the
radius, the “missing” part of the diameter is (2r − x) in length. Using the
fact that one part of one chord times the other part is equal to the same
product taken along a chord intersecting the first chord, we find that
(2r − x)x = (y/2)2. Solving for r, we find the required result.
28. PI
π (sometimes written pi) is a mathematical
constant that is the ratio of any circle's
circumference to its diameter. π is
approximately equal to 3.14. Many formulae
in mathematics, science, and engineering
involve π, which makes it one of the most
important mathematical constants. For
instance, the area of a circle is equal to π
times the square of the radius of the circle
29. π is an irrational number, which means that its
value cannot be expressed exactly as a fraction
having integers in both the numerator and
denominator (unlike 22/7). Consequently, its
decimal representation never ends and never
repeats. π is also a transcendental
number, which implies, among other
things, that no finite sequence of algebraic
operations on integers
(powers, roots, sums, etc.) can render its value;
proving this fact was a significant
mathematical achievement of the 19th century
33. Key facts
•Circumference = the
distance around the
edge of the circle.
•Diameter = a line
across the widest part
of a circle that passes
through the centre.
•Radius = 1/2 the
diameter.
Maybe a drawing will
help you to remember
these facts:
