MathematicsIn a circle of radius 17cm, two parallel chords are drawn on opposite sides of a diameter. The distance between the chords is 23cm. If the length of one chord is 16cm, then the length of the other chord is:

In a circle of radius 17cm, two parallel chords are drawn on opposite sides of a diameter. The distance between the chords is 23cm. If the length of one chord is 16cm, then the length of the other chord is:


  1. A
    34cm
  2. B
    15 cm
  3. C
    23 cm
  4. D
    30cm 

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    Solution:

    It is given that the radius of circle is 17cm.
    And two parallel chords at a distance of 23cm between them, drawn on opposite sides of the diameter.
    Let the diameter cut the chords AB and FD at points E and C respectively.
    Let radius OA=17cm, EC=23cm and AB=16cm.
    We know that the perpendicular from the center to the chord bisects the chord.
    E= 90 o   and AE=EB=8cm.
    In ΔOEA  ,
    By Pythagoras theorem,
    A E 2 +O E 2 =O A 2 O E 2 = 17 2 8 2 O E 2 =28964 O E 2 =225 OE=15cm  
    Now, OC = CE – OE.
    OC = 23 – 15
    OC = 8cm.
    In ΔOCD,
    By Pythagoras theorem,
      O C 2 +C D 2 =O D 2 C D 2 =O D 2 O C 2 C D 2 = 17 2 8 2 C D 2 =28964 C D 2 =225 CD=15cm   We know that the perpendicular from the center to the chord bisects the chord.
    CD =  1 2 FD FD= 2×CD FD = 2×15 FD = 30cm.  
    Therefore, the correct option is (4).
     
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