$\dfrac{\vv{AF}\cdot\vv{AA'}}{\angle A-\angle A'}\to1$

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$AD\perp AB,AE\perp AC,$
$AD=\frac1{AB},AE=\frac1{AC},$
$\vv{AF}=\vv{AD}+\vv{AE},$

求证：当$A'\to A$，$\dfrac{\vv{AF}\cdot\vv{AA'}}{\angle A-\angle A'}\to1$

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$AF$与过$A$的关于$BC$的Apollonian circle相切

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如何证明呢？
如何推广到二面角？