(1) If AO passes through BC to D and O passes through OE⊥BC to E, then △ABD is a regular triangle, OD=4, BD= 12. E is the midpoint of BC, and the angle ODE=60, so DE= 1/2OD=2, BE=CE= 10, BC=20.

(2) If F is FH⊥BC in H, FH=CH= radical number 3*BH, BH+CH= 1, so FH=(3- radical number 3)/2, so CF=(3- radical number 3)/ radical number 2, AF= (radical number 3-60). Similarly, S△CGD=BO*AF/2= (root number 3- 1)/4. S△CEB= radical number 3/4, so S(AFEGD)= 1-2* (radical number 3- 1)/4- radical number 3/4=(6-3 radical number 3)/4.