(1) △OAB为等腰三角形
∠OBA=∠OAB=∠BAE
∴ AE//OB (内错角相等,两直线平行)
(2) ∠OBA=∠OAB=∠BAE=22.5°
∠OAE=∠OEA=45°
∴ ∠AOE=90°
在△OAB中,∠AOB=135°
则 ∠BOC= 45°
得 ∠BCO=45°
BC=OB
OC=OB+CE=√2OB
OB=CE/(√2-1)=√2*(√2+1)=2+√2
△MOB∽△MEA
OB/(√2OB)=OM/ME
ME=√2*MO
ME+OM=OB
ME+√2/2*ME=OB
ME=OB/(1+√2/2)
=2*OB/(2+√2)
=2