(1)相等.
如图:
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/b7003af33a87e9501877e8de13385343fbf2b41b?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
作OG⊥AB于G,OH⊥CD于H,连接OA,OC,OB,OD.
AG=BG,CH=DH,
∵∠EPO=∠FPO,
∴OG=OH.
在Rt△OBG和Rt△ODH中,
由HL定理得:△OBG≌△ODH,
∴GB=HD,
∴AB=CD;
(2)点P在圆上,或在圆内,结论成立.
如图1:
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/342ac65c10385343caaf9c939013b07eca80881b?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
顶点P在圆上,此时点P,A,C重合于点A,作OG⊥AB于G,OH⊥AD于H,
∴AG=GB,AH=HD,
∵∠EAO=∠DAO,
∴OG=OH.
在Rt△OAG和Rt△OAH中,由HL定理得:△OAG≌△OAH,
∴AG=AH,
∴AB=AD.
即点P在圆上,结论成立.
如图2:
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/10dfa9ec8a136327989cd981928fa0ec08fac70b?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
顶点P在圆内,作OG⊥AB于G,OH⊥CD于H,则AG=GB,CH=HD,
∵∠EPO=∠FPO,
∴OG=OH,
∴GB=HD,
∴AB=CD.
即点P在圆内,结论成立.