a) Gọi góc $\widehat{COD}=\alpha \,\,\left( \alpha < 90{}^\circ \right)$

$\widehat{IEG}=\widehat{DOC},\,\,\widehat{HFK}=\widehat{DOC}\Rightarrow \widehat{IEG}=\widehat{HFK\,}\,\,(1)$

$EG=\frac{1}{3}AC,EI=\frac{1}{3}BD\Rightarrow \frac{EG}{EI}=\frac{AC}{BD}\,\,(2)$

Gọi L là giao điểm FK và AC

$FK=FL+LK=AL.\cot \alpha +LC.\cot \alpha =AC.\cot \alpha $

$\Rightarrow \frac{FK}{FH}=\frac{AC}{BD}(3)$

Từ (1), (2) , (3) suy ra $\Delta IEG$ đồng dạng $\Delta HFK$ ( c. g . c )