Mathematical answers to the senior high school entrance examination counseling program
Answer: Proof: As shown in the figure, point O in D is OD⊥AB, and point O in E is OE⊥AC.
∵OD⊥AB，OE⊥AC，AO ∠BAC，
∴OD=OE.？
∵∠ 1=∠2,
∴OB=OC.？
Rt△BDO and Rt△CEO
OD=OEOB=OC，
∴△DOB≌△EOC(HL)，
∴∠DBO=∠ECO，
∴∠ABC=∠ACB，
∴AB=AC.
∫OA segmentation ∠BAC,
∴AO⊥BC.