Xét \(ΔAEC\) và \(ΔADB\):
\(\widehat{EAC}=\widehat{DAB}\)
\(\widehat{AEC}=\widehat{ADB}(=90^\circ\)
\(→ΔAEC\backsim ΔADB(g-g)\)
\(→\dfrac{AD}{AE}=\dfrac{BD}{EC}\) (1)
Xét \(ΔBDI\) và \(ΔCEI\):
\(\widehat{BDI}=\widehat{CEI}(=90^\circ)\)
\(\widehat{BID}=\widehat{CIE}\) (đối đỉnh)
\(→ΔBDI\backsim ΔCEI(g-g)\)
\(→\dfrac{ID}{IE}=\dfrac{BD}{EC}\) (2)
(1)(2) \(→\dfrac{AD}{AE}=\dfrac{ID}{IE}\)