O and Z are the centers of the two circles with radii 7cm and 9cm respectively. The distance between the centres is 20cm. If PQ be the transverse common tangent to the circles, which cuts OZ at X, what is the length of ZX in cm?
(a)35/4
(bb)45/4
(c) 10
(d)11

• ans : b)45/4
  
  explanation:
  from the given scenario we can say,
  ox=20-zx
  we know that,
  The transverse common tangents meet on the line of centres and divide it internally in the ratio of the radii.
  
  so,
  zx/ox=9/7
  =>7zx=9ox
  =>7zx=9(20-zx)
  =>16zx=180
  =>zx=180/16=45/4
  QED...:)
  
  
  
• 11 years agoHelpfull: Yes(34) No(0)
• consider the tangent touches the circle O at P ,Z at Q
  
  here the triangles OPX is Similar to ZQX, Therefore
  
  OP/ZQ=OX/ZX,
  
  ==> 7/9=OX/ZX, adding 1 on both sides
  
  (OX+ZX)/ZX=16/9,(we know that ox+zx=oz=20),
  
  By substituting we get ZX=45/4
• 7 years agoHelpfull: Yes(0) No(0)