O and O' are the center of the two circles with radii 7cm and 3cm resp.the distance between the centers is 20cm .If PQ be the transverse common tangent to the circles, which cuts OO' at X,what is the length of O'X in cm?
A)35/4
B)45/4
C)10
D)11

• if we draw a diagram
  then we can see that there is similar triangles are AOX and BO'X
  applying the property of similar triangle
  7/3 = (20-x)/x
  x=6
• 11 years agoHelpfull: Yes(15) No(6)
• friends replace 3 by 9 you will get right answer i.e 35/4
  @rahul you are right just replace 9 for 3
• 11 years agoHelpfull: Yes(8) No(2)
• Answer will be 45/4.
• 9 years agoHelpfull: Yes(3) No(0)
• i think the options are not right..
• 11 years agoHelpfull: Yes(1) No(1)
• in triangle xop and xo'p
  op/o'p=ox/o'x
  7/3=(20-o'x)/o'x
  70o'x=60-3o'x
  o'x=6
• 11 years agoHelpfull: Yes(1) No(0)
• The transverse common tangents meet on the line of centers and divide it internally in the ratio of the radii. so the answer is 3cm.
• 11 years agoHelpfull: Yes(0) No(6)
• i think option is wrong.. correct ans is 6..
• 11 years agoHelpfull: Yes(0) No(0)
• 
  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
  so answer is 11.25
  
• 10 years agoHelpfull: Yes(0) No(3)
• As clear from the figure itself, triangle OQX and triangle O'PX are similar.
  So,
  OQ/O'P = OX/O'X
  => OX = (7/9)*O'X
  And since, OX + O'X = 20
  => (7/9)*O'X + O'X = 20
  => O'X = 45/4
• 8 years agoHelpfull: Yes(0) No(0)
• By property of similar triangle
  9/7=ox'/(20-ox')
  =>ox'=45/4
• 7 years agoHelpfull: Yes(0) No(0)