Math(f4)-circle Iii 8.1

Chapter

8

CIRCLE III

8.1 (a)

Identify Tangents

What is tangent ? Circle

Straight Line P

A Intersection at point A

Q

When a circle and a straight line intersect at 1 point, we called that line as a tangent. tangent

P

A

Q

Tangent to a circle

Is this a tangent ?

A

Tangent to a circle B

C

Is this a tangent ? X Y

Z

Tangent to a circle

Which are tangents to a circle ? C

A

D

E

Answer : O

Tangent CD at point A Tangent GH at point B F

G

B

H

Which are tangents to a circle ? B H

Answer :

A

Tangent AB at point H

G

Tangent AC at point E E

Tangent BD at point G

F D C

Hiii… Everyone, are you ready to learn the next lesson.. ?

Next concept

Tangent to a circle is perpendicular to the radius of the circle that passes through the contact point .

Radius

P

Q

900 = perpendicular Tangent to a circle

P

Tangent PQ perpendicular with radius OP. O

Tangent RQ perpendicular with radius OR.

R Q

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.

8.1c The Properties Related To Two Tangents From A Given Point Outside The Circle

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. P

O

A

Q

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

PA Value

QA

Angle

∠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,

∠PAO = ∠QAO b) the angle between the two radii that passes through the contact points, that is,

∠POA = ∠QOA

3.∆POA and

∆QOA

are congruent.

P

O

A

Q

SUMMARY A tangent to a circle is a __________ ____________________________ B O

c

O

C

A

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

AB and AC are _______ to the ________ AC BC OBC and OAC are ___________

SUMMARY A tangent to a circle is a straight line which touches the circle at a point. B O

c

O

C

A

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

AB and AC are tangents to the circle. AC = BC OBC and OAC are congruent.