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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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|dw:1358505912245:dw|
interesting :)
can i know what did you attempt here?

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Other answers:

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

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