1. Common Tangents

2. Two circles which intersect at two points
Common Tangents
Two circles which intersect at two points
Common tangent:
AB and CD A B P Q
Properties:
Parallel to PQ
Same length that is
AB = CD C D

3. Two circles which intersect at two points
Common Tangents
Two circles which intersect at two points A B C D F P Q
Common tangent:
AB and CD

4. Two cirlces which intersect at two points
Common Tangents
Two cirlces which intersect at two points A B F P Q D
Properties:
Intersect at point F
AB = CD C

5. Two circles which intersect at only one point
Common Tangents
Two circles which intersect at only one point A B F
Common tangent: AB Q P
Properties:
Perpendicular to FQP

6. Two circles which intersect at only one point
Common Tangents
Two circles which intersect at only one point
Common tangent:
AB and CD A B P Q
Properties:
Parallel to PQ
AB = CD C D

7. Two circles which intersect at only one point
Common Tangents
Two circles which intersect at only one point
Common tangent: EF A E B P Q
Properties:
Perpendicular to PQ C F D

8. Two circles which intersect at only one point
Common Tangents
Two circles which intersect at only one point A
Common tangent:
AB and CD B G P Q D
Properties:
Intersect at point G
AB = CD C

9. Two circles which intersect at only one point
Common Tangents
Two circles which intersect at only one point A
Common tangent: EF E B G P Q D F
Properties:
Perpendicular to PQ C

10. Two circles which do not intersect each other
Common Tangents
Two circles which do not intersect each other
Common tangent:
AB and CD A B P Q
Properties:
Parallel to PQ
AB = CD C D

11. Two circles which do not intersect each other
Common Tangents
Two circles which do not intersect each other
Common tangent:
EH and FG A B E G P Q F H
Properties:
Intersect at line PQ
EH = FG C D

12. Two circles which do not intersect each other
Common Tangents
Two circles which do not intersect each other A B
Common tangent:
AB and CD F P Q C D
Properties:
Intersect at point F
Same length that is AB = CD

13. Two circles which do not intersect each other
Common Tangents
Two circles which do not intersect each other A B
Common tangent:
GH and JK H G K J F P Q C D
Properties:
Intersect at the line PQ
Same length that is GH = JK

14. Common Tangents Solving problems
In the diagram, P and Q are the centres of two circles with radii 9 cm and 4 cm respectively. MN is a common tangent to the circles. Calculate Q M N H P x
(a) the length of MN,
(b) the value of x,
(c) the perimeter of the shaded region.
(Assume  = 3.142)

15. Common Tangents Solving problems P Q T Solution: (a) PQ = 9 + 4
= 13 cm
PT =
9 – 4
= 5 cm P H
In ∆PQT,
TQ2 = PQ2 – PT2 x Q T
= 132 – 52
TQ = 12 cm M N
ஃ MN = 12 cm

16. Common Tangents Solving problems P Q T Solution: (b) tan x = = = 2.4H x Q T M N

17. Common Tangents Solving problems P Q T Solution: (c) Length of arc HM=
× 2 × × 9
= cm
HQN =
180° – 67.4° P
= 112.6° H x
Length of arc HN = Q T
× 2 × × 4
= 7.86 cm M N
Perimeter of the shaded region =
= cm

18. The End