CAT 2018 Question Paper | Quants Slot 1

CAT Questions

This wonderful question from Geometry - Circles appeared in CAT 2018 Question Paper. This question becomes fairly simple if the concept of chords and Pythagoras theorem is clear. Solve and master these types of questions during your CAT Online Preparation to ace the CAT Exam.

Question 30 :In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is

1. √13
2. √14
3. √11
4. √12

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Geometry

Given that Chords lie on the same side of diameter with lengths 4 cms and 6 cms
Draw a perpendicular from the origin to both the chords and mark the points of intersection as P and Q respectively
Consider radius of circle as ‘r’ and distance OP as ‘x’
Draw lines from origin to the end of the chord and mark the points as D and B respectively
Thus, △OQB and △OPD form a right Triangle

Applying Pythagoras Theorem on both triangles,
(x+1)² +2² = r² ---(1)
x² +3² = r² ---(2)
We find that there is an increase and decrease by 1 in both equations
So, x² = 2² , x=2
r²= 2²+3² = 4+9 = 13
r = √13 cms

The question is "In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is"

Hence, the answer is √13 cms

Choice A is the correct answer.