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)

• 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
  
  
• 11 years agoHelpfull: Yes(8) No(1)
• answer is d.
  
  if we draw a figure if tangent is drawn externally.......then it 'll like
  and answer is d
  
  
  
  
• 11 years agoHelpfull: Yes(0) No(4)
• kishor kindly eleborate ...
• 11 years agoHelpfull: Yes(0) No(0)
• @Rohit Kumar
  In terms of CB tangent distance between the centres would be (r0+2r1+r2)
• 7 years agoHelpfull: Yes(0) No(0)
• 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)
• 2 years agoHelpfull: Yes(0) No(0)