Math(F4) Circle Iii 8.1

CIRCLE III8Chapter

8.1 (a)

Identify Tangents

P A Q

CircleCircle

Straight LineStraight Line

Intersection at point AIntersection at point A

What is tangent ?What is tangent ?

When a circle and a straight line intersect at 1 point, we

called that line as a tangenttangent.

P A Q

Tangent to a circleTangent to a circle

Is this a tangent ?

Tangent to a circleTangent to a circle

A

B

C

Is this a tangent ?

Tangent to a circleTangent to a circle

X

Y

Z

Which are tangents to a circle ?

AC D

F

E

O

HBG

Answer :Answer :

Tangent CD at point ATangent CD at point A

Tangent GH at point BTangent GH at point B

Which are tangents to a circle ?

Answer :Answer :

Tangent AB at point HTangent AB at point H

Tangent AC at point ETangent AC at point E

A

E

D

C

B

H

F

G

Tangent BD at point GTangent BD at point G

Hiii… Everyone, Hiii… Everyone, are you ready are you ready

to learn the next to learn the next lesson.. ?lesson.. ?

Next concept

Tangent to a circle is perpendicularperpendicular to the

radius of the circle that passes through the

contact point .

P Q

Tangent to a circleTangent to a circle

RadiusRadius

90900 0 = perpendicular= perpendicular

P

O

RQ

Tangent PQ perpendicularTangent PQ perpendicularwith radius OP.with radius OP.

Tangent RQ perpendicularTangent RQ perpendicularwith radius OR.with radius OR.

8.1 (b)

Construct the tangent to a circle passing

through a point :

a) on the circumference of the circle

b) outside the circle

Activity 1 ( Construct the tangent to a circle

passing through a point on the circumference of the circle )

• Form a group of 5 students.• Complete activity 1 by using

roundtable method.• Time given is 5 minutes.• Then, a student will be chosen to

present the work in front.

Activity 2 ( Construct the tangent to a circle passing through a point outside the

circle )

• Form a group of 5 students.• Complete activity 2 by using

roundtable method.• Time given is 3 minutes.• Then, a student will be chosen to

present the work in front.

The Properties Related To Two

Tangents From A Given Point Outside

The Circle

8.1c

What is The Properties Related To Two

Tangents From A Given Point Outside

The Circle? Let’s do this activity

together

1. Use the previous figure and construct segment from centre to the contact point on the circumference of the circle.

A

P

Q

O

2. Using a ruler and a protractor, measure and record the lengths and angles in table.

Length Angle

Value

PA QA PAO QAO POA QOA

What do you get from this activity?

1. The lengths of the tangent from a given point A to each contact point are equal, PA = QA

2. The line that joins the given point outside the circle, point A, to the centre of the circle bisects.

a) the angle between the two tangents, that is,

b) the angle between the two radii that passes

through the contact points, that is,

QAOPAO

QOAPOA

QOAandPOA 3. are congruent.

A

P

Q

O

SUMMARY

A tangent to a circle is ____________ to the radius drawn through the _________

O

A

cO

B

C

AB and AC are _______ to the ________ AC BC

OBC and OAC are___________

A tangent to a circle is a __________

____________________________

SUMMARY

A

cO

B

C

AB and AC are tangents to the circle. AC = BC

OBC and OAC arecongruent.

A tangent to a circle is perpendicular to the radius drawn through the contact point.

O

A tangent to a circle is a straight line

which touches the circle at a point.