2. Title: An introduction to circles
Author: Deepa. J
Address: Kanjiravila Thekkethil
Puthumala (P.O)
Parakode
Pathanamthitta (Dist)
Cover: Deepa. J
First Edition: 2014
3. ACKNOWLEDGEMENT
I firmly of believed that everything in the world is happening with almighty god.
So first of all I think him for all the care he showed on me.
I wish to express my profound thanks to the people who helped me to make this
book.
There are so many peoples, so many minds all of whom helped me in some way
or other. Neither word can express nor can pages fill the sincere gratitude.
Deepa. J
5. CHAPTER 1
BASIC DEFINITIONS
CIRCLE
A circle is the set of all points in a plane that are at constant distance from a fixed
point. The fixed point is called the ‘centre’ and the constant distance is cal led the
‘radius’.
CENTRE
A point inside the circle and is at an equal distance from all of the points on its
circumference.
RADIUS
The radius is the distance from the centre to any point on the circle.
CHORD
A line segment linking any two points on a circle.
DIAMETER
The distance across the circle. It is a chord which passing through the centre. It is
twice the radius.
6. TANGENT
A tangent to a circle is a line in the plane of the circle that intersects the circle
exactly one point.
SECANT
A secant is a line that intersects a circle at two points.
7. CHAPTER 2
BASIC FORMULAE
PERIMETER
Perimeter of the circle is given by the formula
P= 2 r
Where, P is the perimeter of the circle
r is the radius of the circle.
AREA
Area of a circle is given by the formula
A= r2
Where, A is the area
r is radius of the circle.
EQUATION OF THE CIRCLE
In the co-ordinate system, the equation of the circle with centre (h, k) and radius
‘r’ is
(x- h)2+ (y- k)2= r2
Solution of this equation gives the set of all points (x, y) which are at
constant distance ‘r’ from a fixed point (h, k).
8. CHAPTER 3
EIGHT BASIC THEOREMS
THEOREM 1
The angle at the centre is twice the angle at the circumference.
THEOREM 2
The angle in a semi- circle is 900.
9. THEOREM 3
Angles in the same segment are equal.
THEOREM 4
Opposite angles in a cyclic quadrilateral add up to 1800.
10. THEOREM 5
The lengths of the two tangents from a point to a circle are equal.
THEOREM 6
The angle between a tangent and a radius in circle is 900.
11. THEOREM 7
ALTERNATE SEGMENT THEOREM: The angle between the tangent and chord
at the point of contact is equal to the angle in the alternate segment.
THEOREM 8
Perpendicular from the centre bisects the chord.
