Find the Diameter of the Circle :

AB and CD are two parallel chords of a circle of length 10 cm and 4 cm respectively. If the chords are on the same side of the centre and the distance between then is 3 cm, then the diameter of the circle is

  1. √21 cm
  2.  √29 cm
  3. 2√29 cm
  4.  2√21 cm
Anurag Mishra Professor Asked on 26th October 2015 in Maths.
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  • 1 Answer(s)

    option third is correct.

    Explanation:-
    According to the question,

    RE: Find the Diameter of the Circle :


    In right triangle AOF,
    AO = (X2 + 52)1/2
    CO = {(X + 3)2 + 22}1/2
    AO = CO = radius of the circle

    Then, (X2 + 52)1/2 = {(X + 3)2 + 22}1/2
    square on both side,
    X2 + 52 = (X + 3)2 + 22
     X2 + 25 = X2 + 32 + 2 x 3 x X + 4
    25 = 9 + 4 + 6 X
    6 X = 25 – 13
    6 X = 12
    X = 12/6
    X = 2 cm
    Then, OE = 3 + 2 = 5 cm

    In triangle COE,
    OC = (52 + 22)1/2
    OC = (25 + 4)1/2
    OC = (29)1/2

    Then, the diameter of the circle = 2 x (29)1/2
     = 2(29)1/2 cm

    Hence, the answer is (3) 2(29)1/2 cm.

    Monis Rasool Professor Answered on 28th October 2015.
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