PPT ON CIRCLES

MADE BY :- ATUL MISHRA

CLASS : X H

ROLL NO. : 07

• A circle is the collection of all points in the plane, which are equidistant from a fixed point in the plane.• A circle is a plane figure.• Euclid discovered the circle.•The fixed point is called the centre of the circle • The fixed distance is called the radius of the circle.• The longest chord of the circle is the diameter of the circle.

.O

E

A

B C

D

Given:-EC = CD

TO PROVE :-OB =OA

O IS THE CENTRE OF CIRCLE

CONSTRUCTION:-JOIN OC

“IF THE LENGTH OF TWO CHORDS ARE EQUAL THEN THE ARC IS ALSO EQUAL AND EQUAL ARCS MAKE AN EQUAL ANGLE AT THE CENTRE .”

O is the centre.AB and CD are two equal chords.

TO PROVE:-Angle AOB = Angle COD

PROOF:-In AOB and COD

AO = CO (Radius of circle)

AB = CD (Given) OB = OD (Radius of

circle)By SSS Congruence rule, AOB is congruent to COD By corresponding part of congruent triangle

Angle AOB = Angle COD