Project ID:
5000000059
Accepted:
Template:
Question:
Na obrázku je daná kocka $ABCDEFGH$ s dĺžkou hrany $a= 12\,\mathrm{cm}$, body $K$, $L$ sú po rade stredy hrán $EF$ a $GH$. Určte vzdialenosť medzi
Question Row 1:
\ifen the lines $AB$ and $CD$: \fi \ifcs přímkami $AB$ a $CD$: \fi \ifpl prostymi $AB$ i $CD$: \fi \ifsk priamkami $AB$ a $CD$: \fi \ifes las rectas $AB$ y $CD$: \fi
Answer Row 1:
*{$12\,\mathrm{cm}$}, {$12\sqrt2\,\mathrm{cm}$}, {$12\sqrt3\,\mathrm{cm}$}, {$12\sqrt6\,\mathrm{cm}$}
Question Row 2:
\ifen the lines $AB$ and $KL$: \fi \ifcs přímkami $AB$ a $KL$: \fi \ifpl prostymi $AB$ i $KL$: \fi \ifsk priamkami $AB$ a $KL$: \fi \ifes las rectas $AB$ y $KL$: \fi
Answer Row 2:
{$6\,\mathrm{cm}$}, {$6\sqrt2\,\mathrm{cm}$}, {$6\sqrt3\,\mathrm{cm}$}, *{$12\,\mathrm{cm}$}
Question Row 3:
\ifen the lines $AB$ and $GL$: \fi \ifcs přímkami $AB$ a $GL$: \fi \ifpl prostymi $AB$ i $GL$: \fi \ifsk priamkami $AB$ a $GL$: \fi \ifes las rectas $AB$ y $GL$: \fi
Answer Row 3:
{$12\,\mathrm{cm}$}, *{$12\sqrt2\,\mathrm{cm}$}, {$12\sqrt3\,\mathrm{cm}$}, {$12\sqrt6\,\mathrm{cm}$}
Question Row 4:
\ifen the lines $AB$ and $HK$: \fi \ifcs přímkami $AB$ a $HK$: \fi \ifpl prostymi $AB$ i $HK$: \fi \ifsk priamkami $AB$ a $HK$: \fi \ifes las rectas $AB$ y $HK$: \fi
Answer Row 4:
{$6\,\mathrm{cm}$}, {$6\sqrt2\,\mathrm{cm}$}, {$6\sqrt3\,\mathrm{cm}$}, *{$12\,\mathrm{cm}$}
Question Row 5:
\ifen the line $AB$ and the plane $KFC$: \fi \ifcs přímkou $AB$ a rovinou $KFC$: \fi \ifpl prostą $AB$ i płaszczyzną $KFC$: \fi \ifsk priamkou $AB$ a rovinou $KFC$: \fi \ifes la recta $AB$ y el plano $KFC$: \fi
Answer Row 5:
{$3\,\mathrm{cm}$}, {$6\,\mathrm{cm}$}, *{$6\sqrt2\,\mathrm{cm}$}, {$6\sqrt3\,\mathrm{cm}$}
Question Row 6:
\ifen the line $AB$ and the plane $DCL$: \fi \ifcs přímkou $AB$ a rovinou $DCL$: \fi \ifpl prostą $AB$ i płaszczyzną $DCL$: \fi \ifsk priamkou $AB$ a rovinou $DCL$: \fi \ifes la recta $AB$ y el plano $DCL$: \fi
Answer Row 6:
*{$12\,\mathrm{cm}$}, {$12\sqrt2\,\mathrm{cm}$}, {$12\sqrt3\,\mathrm{cm}$}, {$12\sqrt6\,\mathrm{cm}$}
Tex:
% tiket 33041
\let\oldQuestion\Question
\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=0.2cm]{-1}2{-1}2
{
\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);
\coordinate (K) at ($(E)!0.5!(F)$);
\coordinate (L) at ($(H)!0.5!(G)$);
\draw[thick,dashed] (A) -- (D) node [yshift=-6pt,xshift=3pt]{$D$} -- (C) node [yshift=-5pt,xshift=5pt]{$C$};
\draw[thick,dashed] (D) -- (H);
\draw[thick] (A) node [yshift=-5pt,xshift=-5pt]{$A$} -- (B) node [yshift=-6pt,xshift=3pt]{$B$} -- (F) node [yshift=-6pt,xshift=6pt]{$F$}-- (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);
\begin{scope}[red,thick]
\obrKrizek[2pt]{K}{below right}{K}
\obrKrizek[2pt]{L}{above}{L}
\end{scope}
}
\end{minipage}}
\MsrTabulka[2pt]{0.35\linewidth}{0.55\linewidth}
\pocetsloupcu{4}