a/ Xét \(ΔBDE\) và \(ΔDCE\):
\(\widehat E:chung\)
\(\widehat{BDE}=\widehat{DCE}(=90^\circ)\)
\(→ΔBDE\backsim ΔDCE(g-g)\)
b/ \(CH⊥d,DB⊥d→CH//DB→\widehat{HCE}=\widehat{CBD}\)
Xét \(ΔBCD\) và \(ΔCHE\):
\(\widehat{HCE}=\widehat{CBD}(cmt)\)
\(\widehat{BCD}=\widehat{CHE}(=90^\circ)\)
\(→ΔBCD\backsim ΔCHE\)
\(→\dfrac{BC}{BD}=\dfrac{CH}{CE}\)
\(↔BC.CE=BD.CH\) (1)
Xét \(ΔDCB\) và \(ΔECD\):
\(\widehat{DCB}=\widehat{ECD}(=90^\circ)\)
\(\widehat{BDC}=\widehat{DEC}\) (cùng phụ \(\widehat B\) )
\(→ΔDCB\backsim ΔECD(g-g)\)
\(→\dfrac{DC}{BC}=\dfrac{EC}{DC}\)
\(↔BC.EC=DC^2\) (2)
(1)(2) \(→DC^2=BD.CH\)
