msingh
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.
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msingh
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|dw:1358505912245:dw|
AravindG
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interesting :)
AravindG
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can i know what did you attempt here?
ParthKohli
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can i know what was your attempt here?
msingh
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in a traingle bcd, i apply pythagoras theorem
msingh
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CD^2=BC^2+BD^2
AravindG
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but how you got CD?
msingh
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it is given
msingh
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24^2=BC^2+5^2
AravindG
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ok
AravindG
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ok you see for getting AB we need to take one more triangle.can you tell which one that will be?
msingh
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i don't know
msingh
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AravindG
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well try to think of a triangle containing AB
AravindG
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a right angled one
msingh
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plse see this diagram..
AravindG
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yep i saw
msingh
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do u think taking a triangle BCD is right
msingh
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okay...wait ..the other triangle be ABC.
AravindG
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wait a sec...
AravindG
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to make things clear join OB
AravindG
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where O is centre
msingh
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k
AravindG
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in btw hw did u get bcd as rt angled ? :P
msingh
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that's why i m saying i m wrong , we can't take tr.BCD
Anuska
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ob n od shld b joined
AravindG
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yeh :)
AravindG
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join OA also
AravindG
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i will try my best to draw that
Anuska
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yea thn tk d triangle AOD
Anuska
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& thn apply d theorem
Anuska
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ad^2= oa^2+od^2
AravindG
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@msingh i hand over this one to her :) seeya
msingh
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k
msingh
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vat is value of AD and OA
Anuska
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oa is 5
msingh
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how
msingh
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OA is not a radius
AravindG
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well msing we need to use property of tangents from same point i guess
AravindG
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lemme try this on properly ...
AravindG
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*on paper
sirm3d
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draw a segment joining the centers.
msingh
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|dw:1358508030734:dw|
AravindG
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nice one @sirm3d
sirm3d
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|dw:1358508121964:dw|
AravindG
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isnt OO'=AB @sirm3d ?
sirm3d
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that's right. O'O = AB
AravindG
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ABOO' is a rectangle it seems
AravindG
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my first attempt on this question wasnt as succesful as i thought .well this one was nice :)
AravindG
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@msingh any doubts here?
msingh
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when the triangle are congruent,
vat after that
msingh
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AO'=BO =5cm
CD=24cm
AravindG
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find OO' using that !!
msingh
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CP= CD/2=24/2=12
sirm3d
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OP=12 because the triangles O'CP and ODP are congruent
msingh
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k
sirm3d
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oops. i meant CP=DP =12
AravindG
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Find OP
2OP =OO'
sirm3d
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use pythagorean theorem to find the length of hypotenuse OP of triangle ODP
msingh
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O'P =13cm
msingh
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OO' = 26cm=AB
sirm3d
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right you are!
AravindG
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:) WELL DONE
msingh
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thank u @AravindG and @sirm3d
AravindG
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yw :)
AravindG
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i liked @sirm3d novelty :P
sirm3d
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yw.