Dynamic Geometry: P132

The diagram shows a black circle with radius one. A diameter is drawn. The cyan point travels freely on the circle, which allows us to draw a triangle. The green rectangle is the largest rectangle possible so it is inscribed in the triangle and tangent to the diameter. The center of the rectangle traces a locus (red curve). The area bounded by the red curve can be expressed as $\dfrac{\pi }{p}$ . Find the value of $p$ .