LIC AAO exam question

The radius of the circle is 13 cm and AB is chord which is at a distance of 12 cm from the center. Then the length of the chord is A. 16 cm B. 10 cm C. 8 cm D. 15 cm


4 Respuestas
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4 Respuestas
  • 10 cm

  • 10cm

  • B


  • Let O be the center of Circle and AB be the chord.
    P be the midpoint of AB, So
    AP = PB
    OP = 12 cm = distance of chord from center
    and
    AO = 13 cm = Radius
    Now, OPA forms a right angle triangle.
    Now, by Pythagoras theorem,
    AO^2 = OP^2 + AP^2
    AP^2 = AO^2 - OP^2
    AP^2 = 13^2 - 12^2
    AP^2 = 169 - 144
    AP^2 = 25
    AP = 5 cm.
    Now,
    AB = AP + PB = AP + AP = 5 +5 = 10 cm.