Download presentation

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 = = = 2.4**

H 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

Similar presentations

OK

Summary of Chapter 2 (so far). Parallel lines y = mx + c y = mx + d Perpendicular lines y = mx + cy = nx + dm x n = -1 Length of a line using Pythagoras’

Summary of Chapter 2 (so far). Parallel lines y = mx + c y = mx + d Perpendicular lines y = mx + cy = nx + dm x n = -1 Length of a line using Pythagoras’

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on information technology in agriculture Ppt on eye osmosis Ppt on railway track security system Ppt on 4g lte Micro display ppt on ipad Differential display ppt on ipad Ppt on idiopathic thrombocytopenia purpura Ppt on french culture in french language Ppt on real numbers for class 9th notes Ppt on maggi advertisement