Find radius

Thanks Sir......Never thought about the height of the equilateral triangle in terms of sin
And rahul...Nishant sir's answer is rite.

draw the altitude on this equilateral triangle by drawing radius of these small circles.....

we get two similar triangles...

now apply .....sinA/a = sinB/b = sin C/c

sin30/2r= sin60/4

1/4r=√3/8

2/√3=r

So R = √3 - 1

check that there is a slight mistake in nishant sir's calculation......

.....sinA/a = sinB/b = sin C/c

sin30/2r= sin60/4-2r

1/4r=√3/[2(4-2r)]

8-4r=4√3r

8/4√3+4=r

r= 2/√3+1 r= (√3-1)= ans....

@ venketesha ... u have made mistake in calculations dude....

The answer must be 2/root(3)

The answer in √3 - 1.........Nishant Sir just made a very small mistake in the last step
And rahu....l......The height of the right angle triangle u have drawn in not 4......
It is 4 - 2r

Exactly.... true. true. true......

ya....