Trên tia AD lấy M sao cho \(\widehat{ABC}=\widehat{AMC}\)
Có: \(\Delta ABD\sim\Delta AMC\left(gg\right)\)\(\Rightarrow\frac{AD}{AC}=\frac{AB}{AM}\)
\(\Rightarrow AB.AC=AD.AM\)
Có: \(\Delta ABD\sim\Delta CMD\left(gg\right)\)\(\Rightarrow\frac{AD}{CD}=\frac{BD}{CM}\)
\(\Rightarrow AD.CM=BD.CD\)
\(\Rightarrow AD\left(AM-CM\right)=AD^2=AB.AC-BD.CD\)