Let the radius of yellow semicircle be r,
join the two centers of yellow and blue semicircles and this line intersets them at the point of tangency
hence we get a right triangle with hypotnuese = 18 + r
base =18
perpendicular = 36-r
applying pythagoras theorem we get (18+r)^2 = 18^2 + (36-r)^2
we get r= 12 cms