Lời giải chi tiết:

\( + )\)Xét \(\Delta ABC\)có \(\widehat {ABC} = {90^0}\):

\(A{B^2} + B{C^2} = A{C^2}\) (Định lí Pytago)

\( \Leftrightarrow {1^2} + {1^2} = A{C^2} \Leftrightarrow AC = \sqrt 2 \)

\( \Rightarrow HC = HA = HB = HD = \dfrac{{AC}}{2} = \dfrac{{\sqrt 2 }}{2}\)

\( + )\)Xét \(\Delta SHC\)có \(\widehat {SHC} = {90^0}\):

\(S{H^2} + H{C^2} = S{C^2}\) (Định lí Pytago)

\( \Leftrightarrow {2^2} + {\left( {\dfrac{{\sqrt 2 }}{2}} \right)^2} = S{C^2} \Rightarrow SC = \dfrac{{3\sqrt 2 }}{2}\)

\( \Rightarrow R = \dfrac{{S{C^2}}}{{2.SH}} = \dfrac{{{{\left( {\dfrac{{3\sqrt 2 }}{2}} \right)}^2}}}{{2.2}} = \dfrac{9}{8}\).

Chọn A