Question

# Three balls of equal radius are placed such that they are touching each other. A fourth smaller ball is kept such that it touches the other three.Find the ratio of the radii of smaller to larger ball.

A
(2-√3)/ √3
B
3- 2√3
C
3.5
D
4√5
E
3+2√5

Solution

## The correct option is D (2-√3)/ √3   Option (a) Let the centers of the large balls be x, y, z and radius R. O is the centre of the smaller ball and radius r... x, y, z form an equilateral triangle with side equal to 2R. O is the centroid of this triangle. Therefore ox=oy=oz=R+r= 2/3(height of the triangle xyz) Height=(√3/2)(2R) =√3R Therefore R+r = 2/3(√3R)  =>r/R= (2-√3)/√3   Shortcut:- Using the approximation technique used in class, the radius of the bigger circle: smaller circle is close to 0.2. Free Tests

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