連接OA,OC,OD,AC,AD
令∠X=∠OBC,則cos(X)=(5^2+8^2-5^2)/2*5*8=4/5
則cos(∠ABC)=cos(2X)=2[cos(X)]^2-1=7/25
AC^2=8^2+8^2-2*8*8*cos(2X)=2304/25,則AC=48/5
令∠Y=∠BOC,則cos(Y)=(5^2+5^2-8^2)/2*5*5=-7/25
則cos(∠AOD)=cos(360度-3Y)=cos(3Y)=4[cos(Y)]^3-3*cos(Y)=11753/15625
AD^2=5^2+5^2-2*5*5*cos(3Y)=7744/625,則AD=88/25
所以AC+AD=48/5+88/25=328/25