Chứng minh: A E ⋅ A C = A F ⋅ A B

b) Xét \[\Delta AEB\] và \[\Delta ACF\]có:

\(\widehat {EAB} = \widehat {FAC}\;\,\left( {\widehat A\;\,{\rm{chung}}} \right)\); \(\widehat {AEB} = \widehat {AFC}\;\left( { = 90^\circ } \right)\)

Do đó $\Delta AEB\backsim \Delta ACF\text{\hspace{0.17em}\hspace{0.17em}(g.g)}$

Suy ra \(\frac{{AE}}{{AF}} = \frac{{AB}}{{AC}}\) hay \(AE \cdot AC = AF \cdot AB\) (đpcm)