As shown in figure , it is known that ABCD is parallelogram, A,B,C lie on circle ⊙O1, AD and BD intersect ⊙O at points E and F respectively, C,D,F lie on circle ⊙O2, AD intersects ⊙O2 at point G. If the radii of circles ⊙O1, ⊙O2 are R1,R2 respectively, prove that EGAD=R22R21.