Question

giải chi tiết ạ

Answer 1

\(\widehat{BAH}=\widehat{ACH}\) (cùng phụ góc B)

\(\Rightarrow\Delta BAH\sim\Delta ACH\) theo tỉ số đồng dạng \(k=\dfrac{AH}{CH}\)

Mà \(\dfrac{S_{ABH}}{S_{ACH}}=k^2\Rightarrow\left(\dfrac{AH}{CH}\right)^2=\dfrac{54}{96}\) \(\Rightarrow\dfrac{AH}{CH}=\dfrac{3}{4}\)

\(\Rightarrow AH=\dfrac{3}{4}CH\)

\(S_{ACH}=\dfrac{1}{2}AH.CH=86\Rightarrow\dfrac{1}{2}\left(\dfrac{3}{4}CH\right).CH=96\)

\(\Rightarrow CH^2=256\Rightarrow CH=16\) \(\Rightarrow AH=12\)

\(\Rightarrow BH=\dfrac{2S_{ABH}}{AH}=9\)

\(\Rightarrow R=\dfrac{BH+CH}{2}=12,5\left(cm\right)\)