Quantitative Aptitude – Geometry – Mensuration


Slot – 1 – Quantitative Aptitude – Geometry – Mensuration – In a circle of radius 11 cm, CD is a diameter

Q. In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, is?
  1. 3.5
  2. 1.5
  3. 0.5
  4. 2.5
Answer: 0.5

Solution: As per question following figure can be drawn,

As we know AE*BE = CE*DE
X(20.5 –x) = 7*15 = 105
20.5x –x^2 = 105
x^2 -20.5x + 105 = 0
x^2 -10.5x – 10x +105 =0
(x -10)*(x-10.5) =0
So x = 10 or 10.5
Thus if AE = 10 then BE = 10.5 and vice versa
Required difference = (10.5 -10) = 0.5

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