When statement 1 holds, the length of the wire cant be more than 20 cm. Hence, we have an isoceles triangle of side 5cm, 5cm and 8cm (perimeter=18cm). Hence, the circumradius would be 2.5*2/sqrt(3).
Clearly ,since in the above case, the circumradius is not greater than 4cm , for statement 2 to hold, the sides of the triangle must be 8cm,8cm and 5 cm, in which case, the circumradius would be 4*2/sqrt(3).