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.

Maybe its 4√3/9 .... not sure and confident as Nishant sir's answer is quite different.

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)

U MADE THE same mistake as i did in my earlier post ... the height is 4-2r and not 4..see the figure carefully.........

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....

Maybe this is correct....

but nihal... whts my mistake.... i too got the ans as √3-1