如图所示,在△ABC中,AB=2AC,∠BAD=∠CAD,AD=BD,求证:DC⊥AC

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如图所示,在△ABC中,AB=2AC,∠BAD=∠CAD,AD=BD,求证:DC⊥AC

如图所示,在△ABC中,AB=2AC,∠BAD=∠CAD,AD=BD,求证:DC⊥AC
如图所示,在△ABC中,AB=2AC,∠BAD=∠CAD,AD=BD,求证:DC⊥AC

如图所示,在△ABC中,AB=2AC,∠BAD=∠CAD,AD=BD,求证:DC⊥AC
作DE⊥AB交AB于E,
∵AD=BD,∴AE=BE=½AB,
而AC=½AB,∴AE=AC
又∵∠BAD=∠CAD
∴△AED≌△ACD
∴∠ACD=∠AED=90°,即DC⊥AC.