1. 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 beenobserved, such as the Moon, Sun.3. In
mathematics, the study of the circlehas helped inspire the
development ofgeometry, astronomy, and calculus.
2. A SET OF POINTSWHICH AREEQUIDISTANT FROM AFIXED POINT IS
CALLEDCIRCLE. 3. An arc of a circle is any connected part of
thecircles circumference.A sector is a region bounded by two radii
and anarc lying between the radii.A segment is a region bounded by
a chord and anarc lying between the chords endpoints.A line segment
joining centre and any point on thecircle is called radius. 4.
Circle Area = r2Circumference=2r r = radius 5. The circumference is
the distancearound the outside of a circle.A chord is a line
segment whoseendpoints lie on the circle. A diameteris the longest
chord in a circle. A tangent to a circle is a straight linethat
touches the circle at a singlepoint. A secant is a line passing
through thecircle. 6. orSagitta The sagitta is the vertical
segment. The sagitta (also known as the versine) is a line segment
drawnperpendicular 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 theunique 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 oflength x, since the sagitta intersects the
midpoint of the chord, we knowit 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 thefact 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. 7. PI
(sometimes written pi) is a mathematical constant that is the ratio
of any circles circumference to its diameter. is approximately
equal to 3.14. Many formulae in mathematics, science, and
engineering involve , which makes it one of the most important
mathematical constants. For instance, the area of a circle is equal
to times the square of the radius of the circle 8. is an irrational
number, which means that itsvalue cannot be expressed exactly as a
fractionhaving integers in both the numerator and denominator
(unlike 22/7). Consequently, its decimal representation never ends
and never repeats. is also a transcendentalnumber, which implies,
among otherthings, that no finite sequence of algebraicoperations
on integers(powers, roots, sums, etc.) can render its value;proving
this fact was a significantmathematical achievement of the 19th
century 9. THANK YOUWITH SMILE. 10. Key factsCircumference =
thedistance around theedge of the circle.Diameter = a lineacross
the widest partof a circle that passesthrough the centre.Radius =
1/2 thediameter.Maybe a drawing willhelp you to rememberthese
facts:
