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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

Video Explanation

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.