连结EO、CO.
∵PC切⊙O于C,∴∠PCO＝90°,∴∠OCE＝∠PCO－∠PCD＝90°－∠PCD.
∵PC＝PD,∴∠PCD＝∠PDC,∴∠OCE＝90°－∠PDC.
显然有：∠PDC＝∠ODE,∴∠OCE＝90°－∠ODE,而OC＝OD,∴∠OCE＝∠OEC,
∴∠OEC＝90°－∠ODE,又∠OEC＝180°－∠DOE－∠ODE,∴∠DOE＝90°,
∴AE＝BE,∴∠ABE＝∠BCE.