What is the distance in cm between two parallel cords of length 32cm and 24cm in a circle of radius 20 cm?
1. 4 or 28
2. 2 or 14
3. 1 or 7
4. 3 or 21

• 1. 4 or 28
  let the perpendicular distance of the chords from the center be x & y respectvly
  
  x^2 + 16^2 = 20^2 => x = 12
  y^2 + 12^2 = 20^2 => y = 16
  
  as, chords are parallel, they can same or opposite sides from centre
  distance = 16+12= 28cm or 16-12=4cm
• 10 years agoHelpfull: Yes(59) No(1)
• There are 2 possibilities :
  
  Both chords on opposite side of the centre.
  
  Both side on the same side from the centre.
  
  Opposite side:
  
  Perpendicular from the centre to the chord, bisects the chord.
  
  Hence PB = 12 and QA = 16.
  
  Now apply Pythagoras theorem.
  
  OP^2 = OB^2 - PB^2 = 400 – 144 = 256. OP = 16.
  
  OQ^2 = OA^2 - QA^2 = 400 – 256 = 144. OQ = 12.
  
  Hence, the distance is sum of OP and OQ is 28.
  
  Same side :
  
  We get OP as 16 and OQ as 12 (explained above).
  
  Since they are on the same side, the distance between them is 4. (16 – 12)
  
• 10 years agoHelpfull: Yes(4) No(0)
• chord length=2sqrt(r^2-d^2)
  using these formula find d which is the perpendicular distance
• 10 years agoHelpfull: Yes(1) No(2)
• always remember perpendicular from the center to the chord bisects the chord so using this property we can calulate x distance from one chord to the center by using pythagorus theorem and similarly y distance from another chord and add them you will get 28 as an answer also it may be a possibility that both the chords lie above or below the center in that case just subtract the distance from the individual chord u will achieve 4
• 10 years agoHelpfull: Yes(1) No(0)