anonymous
  • anonymous
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.
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
|dw:1358505912245:dw|
AravindG
  • AravindG
interesting :)
AravindG
  • AravindG
can i know what did you attempt here?

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More answers

ParthKohli
  • ParthKohli
can i know what was your attempt here?
anonymous
  • anonymous
in a traingle bcd, i apply pythagoras theorem
anonymous
  • anonymous
CD^2=BC^2+BD^2
AravindG
  • AravindG
but how you got CD?
anonymous
  • anonymous
it is given
anonymous
  • anonymous
24^2=BC^2+5^2
AravindG
  • AravindG
ok
AravindG
  • AravindG
ok you see for getting AB we need to take one more triangle.can you tell which one that will be?
anonymous
  • anonymous
i don't know
anonymous
  • anonymous
1 Attachment
AravindG
  • AravindG
well try to think of a triangle containing AB
AravindG
  • AravindG
a right angled one
anonymous
  • anonymous
plse see this diagram..
AravindG
  • AravindG
yep i saw
anonymous
  • anonymous
do u think taking a triangle BCD is right
anonymous
  • anonymous
okay...wait ..the other triangle be ABC.
AravindG
  • AravindG
wait a sec...
AravindG
  • AravindG
to make things clear join OB
AravindG
  • AravindG
where O is centre
anonymous
  • anonymous
k
AravindG
  • AravindG
in btw hw did u get bcd as rt angled ? :P
anonymous
  • anonymous
that's why i m saying i m wrong , we can't take tr.BCD
anonymous
  • anonymous
ob n od shld b joined
AravindG
  • AravindG
yeh :)
AravindG
  • AravindG
join OA also
AravindG
  • AravindG
i will try my best to draw that
anonymous
  • anonymous
yea thn tk d triangle AOD
anonymous
  • anonymous
& thn apply d theorem
anonymous
  • anonymous
ad^2= oa^2+od^2
AravindG
  • AravindG
@msingh i hand over this one to her :) seeya
anonymous
  • anonymous
k
anonymous
  • anonymous
vat is value of AD and OA
anonymous
  • anonymous
oa is 5
anonymous
  • anonymous
how
anonymous
  • anonymous
OA is not a radius
AravindG
  • AravindG
well msing we need to use property of tangents from same point i guess
AravindG
  • AravindG
lemme try this on properly ...
AravindG
  • AravindG
*on paper
sirm3d
  • sirm3d
draw a segment joining the centers.
anonymous
  • anonymous
|dw:1358508030734:dw|
AravindG
  • AravindG
nice one @sirm3d
sirm3d
  • sirm3d
|dw:1358508121964:dw|
AravindG
  • AravindG
isnt OO'=AB @sirm3d ?
sirm3d
  • sirm3d
that's right. O'O = AB
AravindG
  • AravindG
ABOO' is a rectangle it seems
AravindG
  • AravindG
my first attempt on this question wasnt as succesful as i thought .well this one was nice :)
AravindG
  • AravindG
@msingh any doubts here?
anonymous
  • anonymous
when the triangle are congruent, vat after that
anonymous
  • anonymous
AO'=BO =5cm CD=24cm
AravindG
  • AravindG
find OO' using that !!
anonymous
  • anonymous
CP= CD/2=24/2=12
sirm3d
  • sirm3d
OP=12 because the triangles O'CP and ODP are congruent
anonymous
  • anonymous
k
sirm3d
  • sirm3d
oops. i meant CP=DP =12
AravindG
  • AravindG
Find OP 2OP =OO'
sirm3d
  • sirm3d
use pythagorean theorem to find the length of hypotenuse OP of triangle ODP
anonymous
  • anonymous
O'P =13cm
anonymous
  • anonymous
OO' = 26cm=AB
sirm3d
  • sirm3d
right you are!
AravindG
  • AravindG
:) WELL DONE
anonymous
  • anonymous
thank u @AravindG and @sirm3d
AravindG
  • AravindG
yw :)
AravindG
  • AravindG
i liked @sirm3d novelty :P
sirm3d
  • sirm3d
yw.

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