A POWERPOIN PRESENTATION ON CIRCLE

What is a circle?• Circles are simple closed curves which divide

the plane into two regions: an interior and an exterior.

Features OF CIRCLE…….

… the distance around the Circle…

… its PERIMETERDiameter

… the distance across the circle, passing through the centre of the circle

Radius

… the distance from the centre of the circle to any point on the circumference

… a line joining two points on the circumference.

… chord divides circle into two segments

… part of the circumference of a circleCho

rd

Tangent

Major Segment

Minor Segment

ARC

… a line which touches the circumference at one point only

From Italian tangere, to touch

Minor Sector

Major sectorSECANT

TANGENT

A tangent to a circle is a line that intersects the circle at only one point

A

B

A tangent is perpendicular to the radius of a circle

THEOREM

THE LENGTH OF TWO TRIANGLES TO A CIRCLE FROM AN EXTERNAL POINT ARE EQUAL AND THEY ARE EQUALLY INCLINED TO THE LINE SEGMENT JOINING THE CENTRE AT THAT POINT

GIVEN: In c(o , r),tangents AP, PB Are shown from the external point P.

To prove: AP=PB, APO= BPO Const.: join AO & BO Proof: In, ∆AOP=∆BOP OP=OP (common) OAP=OBP (Each 90°) AO=OB (radii of same circle) ∆AOP =~ ∆BOP (R.H.S) AP=PB, APO= BPO C.P.C.T HENCE PROVED…..