Conics!

Algebra Level 4

From a point $A$ common tangents are drawn to the circle ${ x }^{ 2 }+{ y }^{ 2 }=2$ and the parabola ${ y }^{ 2 }=8x$ . Find the area of the quadrilateral formed by the common tangents, the chord of contact of the circle and the chord of contact of the parabola.