Semicircle inscribed in other Semicircle
PS is a line segment of length 4 and O is midpoint of PS. A semicircular arc is drawn with PS as diameter. Let X be the midpoint of this arc. Q and R are points on the arc PXS such that QR is parallel to PS and the semicircular arc with QR as diameter is tangent to PS. What is area of the region QXROQ bounded by two semicircular arcs?