Problem

Source: China Northern MO 2008 p5 CNMO

Tags: geometry, parallelogram



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.