Starting with a unit circle (i.e. a circle with radius 1), draw two non-overlapping quadrilaterals inside. The vertices of the quadrilaterals may be on the circle, if you choose. They may also share vertices, edges, or partial edges, but their interirors may not overlap. They may be convex, concave, or one one of each, but may not be crossed (like a bowtie).
What is the largest area these quadrilaterals combined can have?