Because △ABC is rt△ and AC=BC, ∠ bad = 22.5, BD=X/ radical number 5.

Because AC⊥BC, ∠ DAF = 22.5 and ∠ AFB = 67.5, DE=BD/2=X/2 radical number 5.

Because c and d are on the circle, OG⊥CD.

Because AD is the bisector of BAC angle and AD⊥BD, and D is the midpoint of BF.

And g is the midpoint of CD, so DG=DE=X/2 root number 5.

And OD=X/2, god is rt△, so OG=X/ root number 5. OG-DE=3(2- radical number 2), so X=6 radical number 5(2- radical number 2), and the area of the circle o =X*X*π/4=45*(6-4 radical number 2)π.