# A geometry problem by Harshi Singh

Geometry Level 3

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.