Geometry is probably the biggest topic in the CAT syllabus out there. With several concepts & formulas, there are always 3+ questions in CAT previous year paper as well. CAT 2019 question paper was no different. This is a question from the Circles sub topic where a straightforward application on chords is being tested upon. Covering your basics very well in your online CAT Preparation is absolutely vital and this question demonstrates that. If you know one property, you can get the answer, otherwise it is hard.
Question 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
The idea that we use here is remarkably simple.
We know, the product of rectangles formed by two intersecting chords are always equal
So, AE x EB = CE x ED
AE x EB = 7 x 15
Also, we know that AB = 20.5 cms = AE + EB
So, the Sum of AE and EB must be 20.5 and their product must be equal to 7 x 15
7 x 15 = 105
The numbers must be close to each other, for their sum to be 20.5
From trial and error, we find their values to be 10 and 10.5 cms respectively
So, AE x EB = 7 x 15
10 x 10.5 = 7 x 15
Difference = 10.5 - 10 cms = 0.5 cms
The question is "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 "
Choice C is the correct answer.
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