Math(f4)-circle Iii 8.3

RECALL Tangent 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. Q

a)

P

S

R

U

T

b)

Q

R

P

T

S

U

c)

Q

R S

P

B

A

T

U

d) Q

S R

A

B

P

CIRCLES OF THE SAME SIZE a)

Q

P

PQ = RS B

A

PR = QS PQ // RS

R

b)

S

P

T

Q

PQ = RS A

S

B

PR = TU = QS PQ // RS

R

U

S

PR // TU // QS

C) Q

P K

M B

A

N R

L S

PQ = RS, KL = MN, PR = QS PQ // RS, PR // QS

CIRCLES OF DIFFERENT SIZE a)

P Q

A

T

B

S

AP // BQ, AR // BS ABT is a straight line

R

b)

PQ = RS, QT = ST

P

PQ = RS

U Q

QT = ST T

A B S V R

PA // QB, AR // BS ABT is a straight line

c) P

K

Q M T

A

B N

R

L S

PQ = RS, QT = ST, KL = MN PA // QB, AR // BS ABT is a straight line

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

EXAMPLES G

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

P H J

Q A

B L R K

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. D

J

E

A

K

B

F

L

G

a) State the maximum number of common tangents to the circles. b) Find the length of 4c (i) DJ (ii) JL (iii) FG

m 8 cm 8 cm

3

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

D

A

H

B

L Y K

State a)The maximum number common tangents to the 3 G circles. H KL. b)The side which has the same length with A parallel to c)The side which is G (i) BH B L (ii) AK

1P 3E

R

P

E

N

6R

5P

A

A

D I

4C

U L

A

R

Q

I

O

A

U

U

M

L

A

S

M

L

O

E

L 2D

I

S

T

A

N

C

E

L

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

B

A

J F

G Q

P

P Q

E H

D

K C

4 common tangents AB = CD EF = GH PA // QB, PC //QD

L

3 common tangent IJ = KL PI // QJ, PK // QL

A

P

B Q

P Q

D C

2 common tangents AB = CD PA // QB, PC// QD

1 common tangents

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