如图,AC平分∠BAD.AC^2=AB×AD求证:BC^2/CD^2=AB/AD

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如图,AC平分∠BAD.AC^2=AB×AD求证:BC^2/CD^2=AB/AD

如图,AC平分∠BAD.AC^2=AB×AD求证:BC^2/CD^2=AB/AD
如图,AC平分∠BAD.AC^2=AB×AD求证:BC^2/CD^2=AB/AD

如图,AC平分∠BAD.AC^2=AB×AD求证:BC^2/CD^2=AB/AD
证明:
∵AC²=AB×AD
∴AB/AC=AC/AD
又∵∠BAC=∠CAD【AC平分∠BAD】
∴⊿ABC∽⊿ACD
∴BC/CD=AB/AC
BC²/CD²=AB²/AC²=AB²/(AB×AD)=AB/AD