Latest CAT Aptitude Question SOLUTION: O and o' are the centres of the two circles with radii 7 and 9cm respectively. Then distance between the centres is 20cm.if pq be the transverse common tangent to the circles which

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O and o' are the centres of the two circles with radii 7 and 9cm respectively. Then distance between the centres is 20cm.if pq be the transverse common tangent to the circles which cuts oo' at x,what is the lenght of o'x in cm??

Asked In CAT deepika (12 years ago)

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Shireesh Mehta  (10 years ago)

The transverse common tangent divides the line joining the 2 circles in the ratio of their radii i.e. OX:O'X=7:9
The distance separating the circles on the line OO' excluding the radii will be 4 cm [20-7-9].
Let this distance be divided by X in the ratio x:(4-x).
Now, OX=7+(4-x) and O'X=9+x or vice-versa interchanging the 'x' and '4-x' depending on your choice.
We already know that OX:O'X=7:9
Solving for x, we get x=9/4
Hence O'X=9+x=9+(9/4)=45/4

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arivunambi  (12 years ago)

O'X=11.25CM
THEY FORM A SIMILAR TRIANGLE.
SO (7+4-X)/(9+X) =7/9
X=2.25
O'X=X+9=2.25+9=11.25

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Huzefa Chikhly  (11 years ago)

THEY FORM A SIMILAR TRIANGLE.
9/7=(20+7+x)/(7+x)
x=63
o'x=63+7+20= 90

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lakshman chilukuri  (7 years ago)

The transverse common tangent divides the line joining the 2 circles in the ratio of their radii i.e. OX:O'X=7:9
The distance separating the centres is OO=20
since O'X is 9 parts of 16
16---->9
20----->x
x=(20*9)/16
x=11.25

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