Latest TCS Aptitude Question SOLUTION: If three circles are inscribed inside a circle. The radius of the small circles is r. What is the radius of the big circle?

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If three circles are inscribed inside a circle. The radius of the small circles is r. What is the radius of the big circle?

Asked In TCS Varsha (9 years ago)

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RAKESH  (9 years ago)

centres of 3 circles form an eq. triangle of side 2r.

if distance b/n smaller & bigger circle be x
cos30 = r/x => 2r/√3

Radius of bigger circle = r+x = r + 2r/√3 = r(1+ 2/√3)= 2.155r

Is this solution Helpfull? Yes (34) | No (4)  

gautam gaurav  (9 years ago)

let distane of smaller circle to bigger circle is x.
so,cos30=r/x
(3^1/2)/2=r/x
we get x as 1.15r
so radius of bigger circle is r+1.15r=2.15r

Is this solution Helpfull? Yes (5) | No (1)  

Ankita Nema  (9 years ago)

radius of big circle is 2r

Is this solution Helpfull? Yes (2) | No (6)  

NITESH CHANDRA  (9 years ago)

if 3 circles are inscribed in a large circle it forms an equilateral triangle.the center of the large circle becomes the point of intersection of medians of three sides of a triangle..As for equilateral triangle all the sides are equal so the median is same for all i.e,. (√3/2)side of triangle.
therefore (√3/2)2r=√3r
hence radius of the large circle is √3r+r=(√3+1)r
=(1.717+1)r
=2.71r

Is this solution Helpfull? Yes (2) | No   

divyank  (9 years ago)

max 2r ,,just because if 3 small circle inside the big circle take half of the radious of big circle.

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Saddam Hosain  (9 years ago)

@Ankita: better to marry with your answer.....

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uma nath jha  (9 years ago)

r
Bcz all circles may be of same radius

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