a/ \(AB^2=BH.BC=BC\left(BC-CH\right)\)
\(\Leftrightarrow BC^2-2\sqrt{2}BC-16=0\)
\(\Rightarrow BC=4\sqrt{2}\Rightarrow BH=2\sqrt{2}\)
\(AH=\sqrt{AB^2-BH^2}=2\sqrt{2}\)
b/ \(CH-BH=14\Rightarrow CH=BH+14\)
\(AH^2=BH.CH=BH\left(BH+14\right)\)
\(\Rightarrow BH^2+14BH-576=0\Rightarrow BH=18\)
\(\Rightarrow CH=32\Rightarrow BC=BH+CH=50\)
\(AB^2=BH.BC\Rightarrow AB=\sqrt{BH.BC}=30\)
\(AC=\sqrt{BC^2-AB^2}=40\)
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