如图,△ABC中,AB=AC,△ABC的两条中线BC、CE交于O点,求证:OB=OC.

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如图,△ABC中,AB=AC,△ABC的两条中线BC、CE交于O点,求证:OB=OC.

证明:∵AE=AB/2,AD=AC/2,AB=AC
∴AD=AE,∠ABC=∠ACB,
∵AD=AE,∠A=∠A,AB=AC,
∴△ABD≌△ACE,
∴∠ABD=∠ACE,
∴∠ABC-∠ABD=∠ACB-∠ACE,即∠OBC=∠OCB,
∴OB=OC