Question

Answer 1

Xét \(\Delta ABCvà\Delta HBA\) có:

\(\widehat{B}\) chung

\(\widehat{BAC}=\widehat{AHB}=\left(90^o\right)\)

\(\Rightarrow\Delta ABC\) đồng dạng với \(\Delta HBA\)(1)

=> \(\dfrac{AB}{HB}=\dfrac{BC}{AB}\Leftrightarrow AB^2=HB.BC\)

b) Xét \(\Delta ABCvà\Delta HAC\) có:

\(\widehat{C}\) chung

\(\widehat{AHC}=\widehat{BAC}\left(=90^o\right)\)

\(\Rightarrow\Delta ABC\) đồng dạng với \(\Delta HAC\)(2)

\(\Rightarrow\dfrac{AC}{HC}=\dfrac{BC}{AC}\Leftrightarrow AC^2=HC.BC\)

c)Từ (1)(2)  \(\Rightarrow\Delta HBA\) đồng dạng với \(\Delta HAC\)

\(\Rightarrow\dfrac{AH}{CH}=\dfrac{HB}{AH}\Leftrightarrow AH^2=CH.HB\)