如图,BD是∠ABC的角平分线,AB=AC,AB+AD=BC,（1）求∠BAC的度数（2）若F是BD的中点,AE⊥AF于点A,交BD的延长线于点E,求证：BD=2AE

Question

如图,BD是∠ABC的角平分线,AB=AC,AB+AD=BC,（1）求∠BAC的度数（2）若F是BD的中点,AE⊥AF于点A
,交BD的延长线于点E,求证：BD=2AE

Answer 1

延长BA到G,使AG=AD,连接DG,得BG=BC,∠BAC=∠G+∠ADG=2∠G.∵∠DBA=∠DBC,BD=BD,∴ΔBDG≌ΔBDC,∴∠C=∠G,∵AB=AC,∴∠ABC=∠C=∠G=1/2∠BAC,又∠ABC+∠BAC+∠C=180°,∴∠BAC=90°.⑵AF是RTΔABD斜边上的中线,∴AF=...