a.
Xét hai tam giác ABE và ACD có:
\(\left\{{}\begin{matrix}\widehat{ABE}=\widehat{ACD}\left(gt\right)\\\widehat{A}\text{ chung}\end{matrix}\right.\) \(\Rightarrow\Delta ABE\sim\Delta ACD\left(g.g\right)\)
\(\Rightarrow\dfrac{AB}{AC}=\dfrac{AE}{AD}\)
\(\Rightarrow AD.AB=AE.AC\)
b.
Xét hai tam giác OBD và OCE có:
\(\left\{{}\begin{matrix}\widehat{OBD}=\widehat{OCE}\left(gt\right)\\\widehat{DOB}=\widehat{EOC}\left(\text{đối đỉnh}\right)\end{matrix}\right.\)
\(\Rightarrow\Delta OBD\sim\Delta OCE\left(g.g\right)\)
\(\Rightarrow\dfrac{OB}{OC}=\dfrac{OD}{OE}\)
\(\Rightarrow OC.OD=OB.OE\)