BHANWAR LAL GOTHI PUBLIC

SR. SEC. SCHOOL

MATHS

• 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.

theoremIf the length of two chords are equal then their distance from centre is also equal.

.O

E

A

B C

D

Given:-EC = CD

TO PROVE :-OB =OA

O IS THE CENTRE OF CIRCLE

CONSTRUCTION:-JOIN OC

PROOF :-IN BOC AND AOC

L OBC = L OACAC = BCOC = COBY ASS CONGRUENCE RULE

BOC CONGRUENT TO AOCBY CPCT OA = OB

“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

D

C

A

B

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

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