Question 22Eight semicircles line the inside of a square with side length $2$ as shown. What is the radius of the circle tangent to all of these semicircles? $ \dfrac{1+\sqrt2}4$$\dfrac{\sqrt5-1}2$$\dfrac{\sqrt3+1}4 $$\dfrac{2\sqrt3}5 $$\dfrac{\sqrt5}3$
