Đáp án:
$\begin{array}{l}
a)D{E^2} + D{F^2} = {6^2} + {8^2} = 100\\
E{F^2} = {10^2} = 100\\
\Rightarrow D{E^2} + D{F^2} = E{F^2} = 100\\
\Rightarrow \Delta DEF \bot D\\
b){S_{DEF}} = \dfrac{1}{2}.DK.EF = \dfrac{1}{2}.DE.DF\\
\Rightarrow DK = \dfrac{{6.8}}{{10}} = 4,8\left( {cm} \right)\\
D{F^2} = FK.FE\\
\Rightarrow FK = \dfrac{{{8^2}}}{{10}} = 6,4\left( {cm} \right)\\
c)Theo\,t/c:\\
\dfrac{{ME}}{{DE}} = \dfrac{{MF}}{{DF}}\\
\Rightarrow \dfrac{{ME}}{6} = \dfrac{{MF}}{8} = \dfrac{{ME + MF}}{{6 + 8}} = \dfrac{{EF}}{{14}} = \dfrac{5}{7}\\
\Rightarrow \left\{ \begin{array}{l}
MF = \dfrac{{30}}{7}\left( {cm} \right)\\
MF = \dfrac{{40}}{7}\left( {cm} \right)
\end{array} \right.
\end{array}$
