a/ Xét \(ΔBAH\) và \(ΔBCA\):
\(\widehat{B}:chung\)
\(\widehat{BHA}=\widehat{BAC}(=90^\circ)\)
\(→ΔBAH\backsim ΔBCA(g-g)\)
\(→\dfrac{AH}{AB}=\dfrac{CA}{CB}\)
\(↔AH.CB=AB.CA\)
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b/ \(BD\) là đường phân giác \(\widehat{B}\)
\(→\dfrac{DA}{DC}=\dfrac{BA}{BC}\) (1)
Xét \(ΔBAC\) và \(ΔAHC\):
\(\widehat{C}:chung\)
\(\widehat{BAC}=\widehat{AHC}(=90^\circ)\)
\(→ΔBAC\backsim ΔAHC(g-g)\)
\(→\dfrac{BA}{BC}=\dfrac{AH}{AC}\) (2)
(1)(2) \(→\dfrac{DA}{DC}=\dfrac{AH}{AC}\)