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In a circle of radius 11 cm, CD is a diameter - Quantitative Aptitude – Geometry | Circles |

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The question below is from previous year CAT question from CAT 2019 exam comes from CAT Geometry – Circles– In a circle of radius 11 cm, CD is a diameter …

Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2019 – Slot 1 - CAT Circles - Question 5 - In a circle of radius 11 cm, CD is a diameter

Q. 5: 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.   2.5
2.   3.5
3.   0.5
4.   1.5

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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