Project ID:
5000000051
Accepted:
Template:
Question:
The cube $ABCDEFGH$ shown in the picture has edges of length $12\,\mathrm{cm}$. Let $S$ be the midpoint of the base $ABCD$. Find the distance between
Question Row 1:
\ifen the points $E$ and $C$: \fi \ifcs body $E$ a $C$: \fi \ifpl punktami $E$ i $C$: \fi \ifsk bodmi $E$ a $C$: \fi \ifes los puntos $E$ y $C$: \fi
Answer Row 1:
$12\,\mathrm{cm}$, $12\sqrt2\,\mathrm{cm}$, *$12\sqrt3\,\mathrm{cm}$, $12\sqrt6\,\mathrm{cm}$
Question Row 2:
\ifen the points $E$ and $S$: \fi \ifcs body $E$ a $S$: \fi \ifpl punktami $E$ i $S$: \fi \ifsk bodmi $E$ a $S$: \fi \ifes los puntos $E$ y $S$: \fi
Answer Row 2:
$6\,\mathrm{cm}$, $6\sqrt2\,\mathrm{cm}$, $6\sqrt3\,\mathrm{cm}$, *$6\sqrt6\,\mathrm{cm}$
Question Row 3:
\ifen the point $E$ and the line $SC$: \fi \ifcs bodem $E$ a přímkou $SC$: \fi \ifpl punktem $E$ i prostą $SC$: \fi \ifsk bodom $E$ a priamkou $SC$: \fi \ifes el punto $E$ y la recta $SC$: \fi
Answer Row 3:
$6\,\mathrm{cm}$, $6\sqrt2\,\mathrm{cm}$, $6\sqrt3\,\mathrm{cm}$, *$12\,\mathrm{cm}$
Question Row 4:
\ifen the point $E$ and the line $CF$: \fi \ifcs bodem $E$ a přímkou $CF$: \fi \ifpl punktem $E$ i prostą $CF$: \fi \ifsk bodom $E$ a priamkou $CF$: \fi \ifes el punto $E$ y la recta $CF$: \fi
Answer Row 4:
*$12\,\mathrm{cm}$, $12\sqrt2\,\mathrm{cm}$, $12\sqrt3\,\mathrm{cm}$, $12\sqrt6\,\mathrm{cm}$
Question Row 5:
\ifen the point $E$ and the line $CG$: \fi \ifcs bodem $E$ a přímkou $CG$: \fi \ifpl punktem $E$ i prostą $CG$: \fi \ifsk bodom $E$ a priamkou $CG$: \fi \ifes el punto $E$ y la recta $CG$: \fi
Answer Row 5:
$12\,\mathrm{cm}$, *$12\sqrt2\,\mathrm{cm}$, $12\sqrt3\,\mathrm{cm}$, $12\sqrt6\,\mathrm{cm}$
Question Row 6:
\ifen the point $E$ and the plane $BCG$: \fi \ifcs bodem $E$ a rovinou $BCG$: \fi \ifpl punktem $E$ i płaszczyzną $BCG$: \fi \ifsk bodom $E$ a rovinou $BCG$: \fi \ifes el punto $E$ y el plano $BCG$: \fi
Answer Row 6:
*$12\,\mathrm{cm}$, $12\sqrt2\,\mathrm{cm}$, $12\sqrt3\,\mathrm{cm}$, $12\sqrt6\,\mathrm{cm}$
Question Row 7:
\ifen the point $E$ and the plane $SFH$: \fi \ifcs bodem $E$ a rovinou $SFH$: \fi \ifpl punktem $E$ i płaszczyzną $SFH$: \fi \ifsk bodom $E$ a rovinou $SFH$: \fi \ifes el punto $E$ y el plano $SFH$: \fi
Answer Row 7:
$6\,\mathrm{cm}$, *$6\sqrt2\,\mathrm{cm}$, $6\sqrt3\,\mathrm{cm}$, $6\sqrt6\,\mathrm{cm}$
Tex:
% tiket 33040
\let\oldQuestion\Question
\def\I{\mathrm{i}}
\def\Question{
\begin{minipage}[t]{0.6\linewidth}
\leavevmode
\oldQuestion
\end{minipage}
\hfill
\begin{minipage}[t]{0.35\linewidth}
\leavevmode
\kern -20pt
\obrMsr[x=1.5cm,y=1.5cm, z=0.3cm]{-1}2{-1}2
{
\footnotesize
\pgfmathsetmacro{\cubex}{1}
\pgfmathsetmacro{\cubey}{1}
\pgfmathsetmacro{\cubez}{2}
\coordinate (A) at (0,0,0);
\coordinate (B) at (\cubex,0,0);
\coordinate (C) at (\cubex.2,0,\cubez);
\coordinate (D) at (0.2,0,\cubez);
\coordinate (E) at (0,\cubey,0);
\coordinate (F) at (\cubex,\cubey,0);
\coordinate (G) at (\cubex.2,\cubey,\cubez);
\coordinate (H) at (0.2,\cubey,\cubez);
\draw[thick,dashed] (A) -- (D) node [yshift=4pt,xshift=-6pt]{$D$} -- (C) node [yshift=-5pt,xshift=5pt]{$C$};
\draw[thick,dashed] (D) -- (H);
\draw[thick,red,dashed] (A) -- (C);
\draw[thick,red,dashed] (B) -- (D);
\draw[red] (0.6,0,1) node [below,xshift=-2pt,yshift=1pt]{$S$};
\draw[thick] (A) node [yshift=-5pt,xshift=-5pt]{$A$} -- (B) node [yshift=-6pt,xshift=3pt]{$B$} -- (F) node [yshift=6pt,xshift=-3pt]{$F$}-- (E) node [yshift=6pt,xshift=-3pt]{$E$} -- cycle;
\draw[thick] (B) -- (C) -- (G) -- (F);
\draw[thick] (G) node [yshift=6pt,xshift=3pt]{$G$} -- (H) node [yshift=6pt,xshift=-3pt]{$H$} -- (E);
}
\end{minipage}}
\MsrTabulka[1pt]{0.4\linewidth}{0.6\linewidth}
\pocetsloupcu{4}