\(\left\{{}\begin{matrix}\left(SAB\right)\perp\left(ABCD\right)\\\left(SAD\right)\perp\left(ABCD\right)\\\left(SAB\right)\cap\left(SAD\right)=SA\end{matrix}\right.\) \(\Rightarrow SA\perp\left(ABCD\right)\)
\(OM\) cắt (SCD) tại S, mà \(OS=2MS\Rightarrow d\left(M;\left(SCD\right)\right)=\frac{1}{2}d\left(O;\left(SCD\right)\right)\)
\(AO\) cắt (SCD) tại C, mà \(AC=2OC\Rightarrow d\left(O;\left(SCD\right)\right)=\frac{1}{2}d\left(A;\left(SCD\right)\right)\)
\(\Rightarrow d\left(M;\left(SCD\right)\right)=\frac{1}{4}d\left(A;\left(SCD\right)\right)\)
\(\left\{{}\begin{matrix}SA\perp\left(ABCD\right)\Rightarrow SA\perp CD\\CD\perp AD\end{matrix}\right.\) \(\Rightarrow CD\perp\left(SAD\right)\)
Trong mặt phẳng (SAD), từ A kẻ \(AH\perp SD\Rightarrow AH\perp\left(SCD\right)\)
\(\Rightarrow AH=d\left(A;\left(SCD\right)\right)\)
\(\frac{1}{AH^2}=\frac{1}{SA^2}+\frac{1}{AD^2}=\frac{5}{16a^2}\Rightarrow AH=\frac{4a\sqrt{5}}{5}\)
\(\Rightarrow d\left(M;\left(SCD\right)\right)=\frac{1}{4}AH=\frac{a\sqrt{5}}{5}\)
