Xét [tex]\Delta AEF[/tex] và [tex]\Delta ADC:[/tex]
[tex]\frac{AE}{AD}=\frac{3}{4};\frac{AF}{AC}=\frac{6}{8}=\frac{3}{4}\\\Rightarrow \frac{AE}{AD}=\frac{AF}{AC}[/tex]
[tex]\widehat{A}[/tex]là góc chung
[tex]\Rightarrow \Delta AEF[/tex] đồng dạng vs [tex]\Delta ADC[/tex]
[tex]\Rightarrow \widehat{AFE}=\widehat{ACD}\Rightarrow \widehat{DFI}=\widehat{ECI};\widehat{ADC}=\widehat{AEF}\\\widehat{ADC}+\widehat{FDI}=\widehat{AEF}+\widehat{CEI}=180^{o}\\\Rightarrow \widehat{FDI}=\widehat{CEI}[/tex]
Xét [tex]\Delta IDF[/tex] và [tex]\Delta IEC:[/tex]
[tex]\widehat{DFI}=\widehat{ECI}\\\widehat{FDI}=\widehat{CEI}[/tex]
[tex]\Rightarrow \Delta IDE[/tex] đồng dạng vs [tex]\Delta IEC[/tex]
[tex]\Rightarrow \frac{ID}{IE}=\frac{IF}{IC}=\frac{DF}{EC}=\frac{6-4}{8-3}=\frac{2}{5}\\\Rightarrow \frac{ID}{IE}=\frac{IF}{IC}=\frac{DF}{EC}=\frac{ID+IF+DF}{IE+IC+EC}=\frac{2+2+2}{5+5+5}=\frac{2}{5}\\\Rightarrow \dfrac{C_{IDF}}{C_{IEC}}=\frac{2}{5}[/tex]