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.
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= 23(height of the triangle xyz)
Height=(√32)(2R) =√3R
Therefore R+r =23(√3R) ⇒rR= (2−√3)√3