1.连BD,AC,则∠CAB为直角.
∵AB⌒=AD⌒,∴∠BCA=∠ACE.
在△EDA与△ABC中,∠EAD=∠ACE=∠ACB.
又∠EDA与∠ABC都与∠ADC互补,
∴∠EDA=∠ABC.因此,△EDA∽△ABC.
∴∠AED=∠CAB=90°.
∴△AED是直角三角形.
2.∵ED;EA=1:2,∴∴AB:AC=1:2.
∵AD=AB=2√5,∴AC=2AB=4√5,
BC^2=AB^2+AC^2=20+80=100,∴BC=10.
3.∵∠CDA与∠ABC互补,
∴sinCAD=sinABC=AC/BC=(4√5)/10=2√5/5.