Kẻ HM vuông góc BC ( M thuộc BC )
\(\Delta BHM~\Delta BCD\left(g.g\right)\) \(\Rightarrow\frac{BH}{BC}=\frac{BM}{BD}\Rightarrow BH.BD=BC.BM\) ( 1 )
\(\Delta CHM~\Delta CBE\left(g.g\right)\Rightarrow\frac{CH}{BC}=\frac{CM}{CE}\Rightarrow CH.CE=BC.CM\) ( 2 )
Từ ( 1 ) và ( 2 ) \(\Rightarrow BH.BD+CH.CE=BC\left(BM+CM\right)=BC^2\)