GEOMETRY

Circle Terminology

Component of Geometry

• Point (dot)• Line At least two points given• Angle If two line intersect in a point• Plane Something which has area• Space something which boundary at least

by two plane

Circle

• Set of points which have same distance into one permanent point

Same distance = radius = rPermanent point is central point

Radius (or Radii for plural)

• The segment joining the center of a circle to a point on the circle.

• Example: OAO

A

adopted from http://www.worldofteaching.com

Diameter

• A chord that passes through the center of a circle.

• Example: AB• What is AO?• What is OB?• What is relation between radius and

diameter?

O

A

BRadius Radius

d=2r

Chord

• A segment joining two points on a circle

• Example: AB

B

CA

Chord

• A segment joining two points on a circle

• Example: AB• AB= diameter• So, what is relation between chord and

diameter?

B

C

A

Diameter is the longest chord

Secant

• A line that intersects the circle at exactly two points.

• Example: AB

D

C

B

A

O

Secant

• A line that intersects the circle at exactly two points.

• Example: AB

D

C

B

A

O

Tangent

• A line that intersects a circle at exactly one point.

• Example: AB

C

B

A

Central Angle

• An angle whose vertex is at the center of a circle.

• Example: Angle ABC

A

B

C

Inscribed Angle

• An angle whose vertex is on a circle and whose sides are determined by two chords.

• Example: Angle ABC

AB

C

Arc

• A figure consisting of two points on a circle and all the points on the circle needed to connect them by a single path.

• Example: arc AB

A

B

What is the longest arc? circumference

Intercepted Arc

• An arc that lies in the interior of an inscribed angle.

• Example: arc AC

AB

C

Two Intercepted Arc

• If angle is inside the circle.

• Example: arc AC arc DF

B

F

A

D

C

• If angle is outside the circle.

• Example: arc DE arc DC

Two Intercepted Arc

E

D

B

A

C

Apothem

• The shortest distance between center point and chord

• Example: OAA

Segment

• Area which bordered by arc and chord

• Shaded area is minor segment

• Plain area is major segmentO

Sector

• Area which bordered by two radii and an arc

• Shaded area is minor sector

• Plain area is major sector

O

Requirements:-• Compass• Pencils• Eraser• Scale• Set Square

If line touches the circle at one point only that is called a tangent

If line connect the two point at the circle that is called a chord

If line intersect the circle at two point that is called secant

Formation of tangent

Circle

AB

SecantC

D

Chord

PTangent

APB is called a tangent to the circle The touching point P is called the point of contact.

C

A

B

P

AB

CD

E

FG

H

P Q

We construct four tangents AB,CD, EF & GH

When two circles do not touch

AB

CD

OO’

..

We can construct three tangents APB, CQD, PRQ

When two circles touches externally

P

Q

1st Tangent

2nd Tangent

3rd Tangent

R

When two circles intersect each other

A B

CD

1st Tangent

2nd Tangent

O O!. .

We can construct two tangents AB, CD

A

B

O O’

When two circles touches internally

We can construct only one tangents APB

P

When two concurrent circles

OO’

We can not construct any common tangent

P

P is a point out side the circle you can construct two tangents passing through P

O

Q

R

Tangent PQ = TangentPR

A B

C

o

Constructing Circumcircle

Steps of Construction

Construct a Δ ABC

Bisect the side AB

Bisect the side BC

The two lines meet at O

From O Join B

Taking OB as radius draw a circumcircle.

A B

C

Constructing of incircle

Steps of construction

Construct a Δ ABC

The two lines meet at O

Taking OP as radius Draw a circumcircle

Bisect the ABCBisect the BAC

Taking O draw OP AB

O

P