What is the distance between two parallel chords of length 24 cm and 32 cm in a cirle of radius 20 cm ?

(a) 4 or 28
(b) 1 or 7
(c) 2 or 14
(d) 3 or 21

• There are two possibilities: Either the chords are on the opposite side of the diameter OR on the same side.
  Let the distances of the chords 24cm and 32cm from the center be x&y.
  x^2+12^2=20^2 i.e x=16
  y^2+16^2=20^2 i.e y=12
  Thus, distance between the chords can be 16+12=28cm or 16-12=4cm....option(a)
• 9 years agoHelpfull: Yes(16) No(1)
• suppose that given chords are parallel to diameter of circle
  chord ab=24
  chord cd=32
  let m is perpendicular to ab from centre o such that am=mb
  let n is perpendicular to cd from centre o such that cn=nd
  in tringle omb and ond ob=od=radius of circle=20
  in tringle omb mb=ab/2=12
  so om=sqrt(ob,mb)=16
  in tringle ond nd=cd/2=24
  so on=sqrt(od,nd)=12
  so distance b/w both chord:
  if they are in one side of diameter=om-on=4
  if they are in opposite side of diameter=om+on=28
  so correct option is (a)
• 9 years agoHelpfull: Yes(3) No(0)
• Radius of Circle 20
  First Chord length=24
  Distance1=Sqrt(20*20-12*12)
  Second Chord length=32
  Distance2=Sqrt(20*20-16*16)
  Distance=Distance1+Distance2
  or Distance=Distance1-Distance2
  Ans a
• 9 years agoHelpfull: Yes(1) No(0)
• R1=32 and R2=24
  So R1/2+R2/2 or R1/2-R2/2 i.e 16-12=4 or 16+12=28
  So ans is 4or28
  
• 9 years agoHelpfull: Yes(1) No(0)
• simply by using Pythagorean theorem we can calculate this taking half of both cords as base and perpendicular on center as height.
  then subtracting both answers we get needed distance.
• 9 years agoHelpfull: Yes(1) No(0)
• please draw the circle and chords
• 9 years agoHelpfull: Yes(0) No(0)
• form two triangles, OAB and OCD
  OA,OB,OC,OD=circle radius
  DISTANCE= sqrt(400-144)+sqrt(400-256)=27
  sqrt(400-144)-sqrt(400-256)=4
• 9 years agoHelpfull: Yes(0) No(0)