Latest Elitmus Aptitude Question SOLUTION: 3 circles touching each other.smaller circle having radius r0 and other two larger circle having radius r1,r2 and there is a common tangent to all three.find 1/r0 a)(1/r1+1/r2) b)(

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(#M40024319) ELITMUS Numerical Ability question asked on 29 september Keep an EYE

3 circles touching each other.smaller circle having radius r0 and other two larger circle having radius r1,r2 and there is a common tangent to all three.find 1/r0
a)(1/r1+1/r2)
b)(1/r1+1/r2)^2
c)(1/r1^1/2 +1/r2^1/2)^2
d)(1/r1^1/2 +1/r2^1/2)

Asked In Elitmus rohit kumar (10 years ago)

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rohit kumar  (10 years ago)

answer will be c
draw the figure
length of tangent between circle of radius r1 and r2 is {(r1+r2)^2+(r1-r2)^2}^1/2
from the formula of common tangent length
solving this we will get let say this AB= 2(r1*r2)^1/2
similary for other we will get AC= 2(r0*r1)^1/2 and CB= 2(r0*r2)^1/2
solving this equation as AB=BC+CB
we will get 1/(r0)^1/2=1/(r1)^1/2+1/(r2)^1/2
solving for 1/r0
we will get (1/r1^1/2 +1/r2^1/2)^2

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KISHOR KUNAL  (10 years ago)

answer is d.

if we draw a figure if tangent is drawn externally.......then it 'll like
and answer is d

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saurabh prakash  (10 years ago)

kishor kindly eleborate ...

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Prasanna Pradhan  (6 years ago)

@Rohit Kumar
In terms of CB tangent distance between the centres would be (r0+2r1+r2)

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Digesh Singh Bisht  (1 year ago)

Ans is D.
As there is a theorem in Geometry Topic, which states that if a line is common tangent to 3 circles then
the smaller circle radius(r0) will always be equal to = ((1/r1)sqrt +(1/r2)sqrt)

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