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.

- anonymous

- jamiebookeater

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- anonymous

|dw:1358505912245:dw|

- AravindG

interesting :)

- AravindG

can i know what did you attempt here?

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## More answers

- ParthKohli

can i know what was your attempt here?

- anonymous

in a traingle bcd, i apply pythagoras theorem

- anonymous

CD^2=BC^2+BD^2

- AravindG

but how you got CD?

- anonymous

it is given

- anonymous

24^2=BC^2+5^2

- AravindG

ok

- AravindG

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

- anonymous

i don't know

- anonymous

##### 1 Attachment

- AravindG

well try to think of a triangle containing AB

- AravindG

a right angled one

- anonymous

plse see this diagram..

- AravindG

yep i saw

- anonymous

do u think taking a triangle BCD is right

- anonymous

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

- AravindG

wait a sec...

- AravindG

to make things clear join OB

- AravindG

where O is centre

- anonymous

k

- AravindG

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

- anonymous

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

- anonymous

ob n od shld b joined

- AravindG

yeh :)

- AravindG

join OA also

- AravindG

i will try my best to draw that

- anonymous

yea thn tk d triangle AOD

- anonymous

& thn apply d theorem

- anonymous

ad^2= oa^2+od^2

- AravindG

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

- anonymous

k

- anonymous

vat is value of AD and OA

- anonymous

oa is 5

- anonymous

how

- anonymous

OA is not a radius

- AravindG

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

- AravindG

lemme try this on properly ...

- AravindG

*on paper

- sirm3d

draw a segment joining the centers.

- anonymous

|dw:1358508030734:dw|

- AravindG

nice one @sirm3d

- sirm3d

|dw:1358508121964:dw|

- AravindG

isnt OO'=AB @sirm3d ?

- sirm3d

that's right. O'O = AB

- AravindG

ABOO' is a rectangle it seems

- AravindG

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

- AravindG

@msingh any doubts here?

- anonymous

when the triangle are congruent,
vat after that

- anonymous

AO'=BO =5cm
CD=24cm

- AravindG

find OO' using that !!

- anonymous

CP= CD/2=24/2=12

- sirm3d

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

- anonymous

k

- sirm3d

oops. i meant CP=DP =12

- AravindG

Find OP
2OP =OO'

- sirm3d

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

- anonymous

O'P =13cm

- anonymous

OO' = 26cm=AB

- sirm3d

right you are!

- AravindG

:) WELL DONE

- anonymous

thank u @AravindG and @sirm3d

- AravindG

yw :)

- AravindG

i liked @sirm3d novelty :P

- sirm3d

yw.

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