Question

一道初三圆的证明题!请帮忙～如图,在△ABC中,AB=AC,过点A的直线与△ABC外接圆O交于点D,与BC的延长线交于点

Answer 1

（2）在△ACF和△ADC中,∵∠CDF=∠ABC=∠ACB,

∴∠ACF=∠ADC.

∵∠CAF=∠DAC,

∴△ACF∽△ADC

∴AC/AD=AF/AC,即AC^2=AD·AF.

∵AB=AC,

∴AB^2=AD·AF

∴AF^2-AB^2=AF^2-AD·AF=AF（AF-AD）=AF·DF

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