Circle Theory. 2x2x x This is the ARC o Centre of Circle The Angle x subtended at the centre of a...

Circle Theory

2x

x

This is the ARC

o

Centre of Circle

The Angle x subtended at the centre of a circle by an arc is twice the size of the angle on the circumference subtended by the same arc.

2x

x

o

This is the ARC

Centre of Circle

Angle subtended at the Centre is twice the angle at the circumference

x

x

x

We are ALL EQUAL

This is the Arc

Minor Segment

Major Segment

o

A

B

CDx

180-x

If this angle was 600 then angle BCD would be 1800-600=1200

1200

Points which lie on the circumference of the same circle are called cyclic (or concyclic)points. A cyclic quadrilateral is a quadrilateralwith all its four corners (vertices) on thecircumference of the same circle.

T

A

B

O

TA=TB

Tangent

Tangent

Major Segment

Minor SegmentA B C

E

D

The Shaded Segment BED is called the alternate segment to the angle CBDThe angle between a tangent to a circle and a chord drawn through the pointof contact is equal to any angle subtended by the chord at the circumference in the alternate segment

Center of Circle

Diameter