如图,∠AOD=90°,OA=OB=BC=CD,求证(1)∠BAC=∠ADB (2)∠ACB=∠BAD

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如图,∠AOD=90°,OA=OB=BC=CD,求证(1)∠BAC=∠ADB (2)∠ACB=∠BAD

如图,∠AOD=90°,OA=OB=BC=CD,求证(1)∠BAC=∠ADB (2)∠ACB=∠BAD
如图,∠AOD=90°,OA=OB=BC=CD,求证(1)∠BAC=∠ADB (2)∠ACB=∠BAD

如图,∠AOD=90°,OA=OB=BC=CD,求证(1)∠BAC=∠ADB (2)∠ACB=∠BAD
(1)∵OA=OB=BC=CD,∠AOD=90°
∴AB=√(OA^2+OB^2)=√2*OA
AC=√(OA^2+CO^)=√5*OA
AD=√(OA^2+DO^)=√10*OA
AD/AC=√10*OA/(√5*OA)=√2
BD/AB=2*OA/(√2*OA)=√2
∴AD/AC= BD/AB
∴ΔADB∽ΔCAB
∴∠BAC=∠ADB
(2) ∵∠BAC=∠ADB
∠ACB=∠ADB+∠DAC
∴∠ACB=∠BAC+∠DAC
=∠BAD