a/ Kẻ \(CE//BD\Rightarrow BD//\left(SCE\right)\Rightarrow d\left(SC,BD\right)=d\left(BD,\left(SCE\right)\right)=d\left(B,\left(SCE\right)\right)\)
\(AB\cap\left(SCE\right)=\left\{E\right\}\Rightarrow\dfrac{d\left(B,\left(SCE\right)\right)}{d\left(A,\left(SCE\right)\right)}=\dfrac{EB}{EA}=\dfrac{1}{2}\)
\(\widehat{CAE}=\dfrac{1}{2}\widehat{DAB};\widehat{AEC}=\widehat{BDC}=\dfrac{1}{2}\widehat{ADC};\widehat{DAB}+\widehat{ADC}=180^0\Rightarrow\widehat{CAE}+\widehat{AEC}=90^0\Rightarrow\widehat{ACE}=90^0\)
\(\Rightarrow AC\perp EC\)
\(\left\{{}\begin{matrix}SA\perp CE\\AC\perp CE\end{matrix}\right.\Rightarrow CE\perp\left(SAC\right)\Rightarrow\left(SCE\right)\perp\left(SAC\right)\)
Kẻ \(AH\perp SC\Rightarrow AH\perp\left(SCE\right)\Rightarrow d\left(A,\left(SCE\right)\right)=AH=\dfrac{SA.AC}{\sqrt{SA^2+AC^2}}=..\)
\(\Rightarrow d\left(SC,BD\right)=d\left(B,\left(SCE\right)\right)=\dfrac{AH}{2}=...\)
b/ \(AD//BC\Rightarrow AD//\left(SBC\right)\Rightarrow d\left(SC,AD\right)=d\left(AD,\left(SBC\right)\right)=d\left(A,\left(SBC\right)\right)\)
Kẻ \(AK\perp BC\Rightarrow\left\{{}\begin{matrix}SA\perp BC\\AK\perp BC\end{matrix}\right.\Rightarrow\left(SBC\right)\perp\left(SAK\right)\)
Kẻ \(AM\perp SK\Rightarrow AM\perp\left(SBC\right)\Rightarrow d\left(A,\left(SBC\right)\right)=AM=\dfrac{SA.AK}{\sqrt{SA^2+AK^2}}=...=d\left(SC,AD\right)\)
