A geometry problem by Harshi Singh

Given that the radius of larger circle is $R =2$ , find the radius of smaller circle, i.e. $r=?$

Details and assumptions :-

• The smaller circle is tangent to :-

$1)$ The arc which subtends an angle of $60^\circ$ in the opposite arc.

$2)$ The two radii that join endpoints of the arc to the center of the circle.

• Round your answer to 2 decimal places.