Circle is defined as the set of all points in a plane that are equidistant from a fixed point called the center. A radius is a line segment from the center to any point on the circle, while a diameter is a line segment going through the center that spans one side of the circle to the other. A chord is a line segment connecting any two points on the circle. The perpendicular from the center to a chord passes through the midpoint of the chord. Chords of equal length must be equidistant from the center.

1. CIRCLES

2. Circle is the collection of points in a plane that are all the
same distance from a fixed point.
The fixed point is called the center.

3. The diameter starts at one side of the circle, goes
through the center and ends on the other side.
A line segment joining the center to any point on
the circle is called radius.

4. A line joining any pair of points on a circle, is
called a chord of the circle.
The longest chord DB, is called the diameter of
the circle.
AB,DB,CD are the chords of the circle

5. The perpendicular from the center of a circle to a
chord, passes through the midpoint of the chord.

6. Prove that in a circle , chords of equal length are at equal
distance from the center ?
AE,BF are chords of equal length and OC, OD
are perpendicular from the center O of the
circle to these chords.
We have ,AC = ½ AE and BD = ½ BF
Since ,AE = BF. We get , AC = BD

7. From the right angled triangle OAC, OBD ,
We get, OC2 = OA2 – AC2
OD2 = OB2 – BD2
Since, OA = OB (radius )
AC = BD
,
We get, OC2 = OD2
And so OC = OD