Math(F4)-Circle III 8.3

RECALLTangent to a circle.

At the end of this lesson, student able to :

State the number of common tangents to two circles.

State the properties related to the common tangents to two circles.

Definition Of Common Tangent To Two Circle

Exercise State the maximum number of common tangents to the circle.

a)

P

Q

RS

T

U

b)

P

Q

R

ST

U

c)

BA

P

QR

S

T

U

d)

BA

P

Q

R

S

PQ = RS

PR = QS

PQ // RS

PQ = RS

PR = TU = QS

PQ // RS

PR // TU // QSU

T

S

S

B

P

R

A

Q

S

B

P

A

R

Q

i) CIRCLES OF THE SAME SIZEa)

b)

PQ = RS, KL = MN, PR = QS

PQ // RS, PR // QS

N L

K

S

B

P

A

R

QM

C)

S

R

BA

P

Q

T

V

U

S

R

BA

P

Q

T

PQ = RS,QT = ST

AP // BQ, AR // BS

ABT is a straight line

PQ = RS

QT = ST

PA // QB, AR // BS

ABT is a straight line

ii ) CIRCLES OF DIFFERENT SIZEa)

b)

N

M

S

R

BA

P

Q

T

K

L

PQ = RS, QT = ST, KL = MN

PA // QB, AR // BS

ABT is a straight line

c)

The distance between the contact points of corresponding common tangents are equal

For two circles of different sizes, the corresponding common tangents meet at a points on the straight line that passes through the centres of the circles

The radii of two circles drawn from the respective contact points of a common tangent are parallel

In the case of two circles intersecting at only one point, the tangent passing through the point of intersection is perpendicular to the line joining the centres of the circles

In the figure, points A and B are the centres of two circles. Identify and state

(a)The three common tangents to the two circles.(b)The side which has the same length as

(i) GH (ii) LJ

R

P

Q

L

K

BA

G

H

J

EXAMPLES

Solution

a)Common tangents are GPHJ, KRLJ and PQR.

b)(i)GH = KL (ii)LJ = HJ

1) The figure shows two circles with centres A and B respectively. Their radii are 4 cm.

L

J

K

G

B

D

A

F

E

a) State the maximum number of common tangents to the circles. b) Find the length of(i) DJ

(ii) JL

(iii) FG

3

4cm

8 cm

8 cm

State a)The maximum number common tangents to the circles. b)The side which has the same length with KL. c)The side which is parallel to (i) BH (ii) AK

2) The figure shows common tangents to two circles with centres A and B.

Y

X

L

K

DA

G

H

B

3GH

AG

BL

6R 5P

A A

1P 3E R P E N D I 4C U L A R

Q I O A

U U M L

A S M L

L O E

2D I S T A N C E L

L

I

J

P

Q

K

D

B

P

Q

A

C

E

F

H

G

COMMON TANGENT TO TWO CIRCLESA straight line that touches each of the circles at only one point.

4 common tangentsAB = CDEF = GHPA // QB, PC //QD

3 common tangentIJ = KLPI // QJ, PK // QL

D

B

P Q

A

C

2 common tangents AB = CDPA // QB, PC// QD

1 common tangents

P

Q

HOMEWORK Page 217, No. 1 - 4