A designer wants to design a new company logo. She decides that the logo will consist of a circle with two regular polygons drawn inside it. The vertices of the regular polygons all lie on the circumference of the circle. 

a. If the final logo has four lines of symmetry and a rotational symmetry of order four, which possible regular polygons has the designer used? 

b. Is there another possible combination of two regular polygons, other than those you stated in (a) above, that the designer could have used? Give a convincing answer. 

c. Sketch a possible logo drawn by the designer.