## msingh 2 years ago two equal circles of radius 5 cm have two common tangent AB and CD which touch the circle on A, C and B, D respectively and if CD = 24 cm, find the length of AB.

1. msingh

|dw:1358505912245:dw|

2. AravindG

interesting :)

3. AravindG

can i know what did you attempt here?

4. ParthKohli

can i know what was your attempt here?

5. msingh

in a traingle bcd, i apply pythagoras theorem

6. msingh

CD^2=BC^2+BD^2

7. AravindG

but how you got CD?

8. msingh

it is given

9. msingh

24^2=BC^2+5^2

10. AravindG

ok

11. AravindG

ok you see for getting AB we need to take one more triangle.can you tell which one that will be?

12. msingh

i don't know

13. msingh

14. AravindG

well try to think of a triangle containing AB

15. AravindG

a right angled one

16. msingh

plse see this diagram..

17. AravindG

yep i saw

18. msingh

do u think taking a triangle BCD is right

19. msingh

okay...wait ..the other triangle be ABC.

20. AravindG

wait a sec...

21. AravindG

to make things clear join OB

22. AravindG

where O is centre

23. msingh

k

24. AravindG

in btw hw did u get bcd as rt angled ? :P

25. msingh

that's why i m saying i m wrong , we can't take tr.BCD

26. Anuska

ob n od shld b joined

27. AravindG

yeh :)

28. AravindG

join OA also

29. AravindG

i will try my best to draw that

30. Anuska

yea thn tk d triangle AOD

31. Anuska

& thn apply d theorem

32. Anuska

33. AravindG

@msingh i hand over this one to her :) seeya

34. msingh

k

35. msingh

vat is value of AD and OA

36. Anuska

oa is 5

37. msingh

how

38. msingh

39. AravindG

well msing we need to use property of tangents from same point i guess

40. AravindG

lemme try this on properly ...

41. AravindG

*on paper

42. sirm3d

draw a segment joining the centers.

43. msingh

|dw:1358508030734:dw|

44. AravindG

nice one @sirm3d

45. sirm3d

|dw:1358508121964:dw|

46. AravindG

isnt OO'=AB @sirm3d ?

47. sirm3d

that's right. O'O = AB

48. AravindG

ABOO' is a rectangle it seems

49. AravindG

my first attempt on this question wasnt as succesful as i thought .well this one was nice :)

50. AravindG

@msingh any doubts here?

51. msingh

when the triangle are congruent, vat after that

52. msingh

AO'=BO =5cm CD=24cm

53. AravindG

find OO' using that !!

54. msingh

CP= CD/2=24/2=12

55. sirm3d

OP=12 because the triangles O'CP and ODP are congruent

56. msingh

k

57. sirm3d

oops. i meant CP=DP =12

58. AravindG

Find OP 2OP =OO'

59. sirm3d

use pythagorean theorem to find the length of hypotenuse OP of triangle ODP

60. msingh

O'P =13cm

61. msingh

OO' = 26cm=AB

62. sirm3d

right you are!

63. AravindG

:) WELL DONE

64. msingh

thank u @AravindG and @sirm3d

65. AravindG

yw :)

66. AravindG

i liked @sirm3d novelty :P

67. sirm3d

yw.