Đáp án:
$\begin{array}{l}
Theo\,Pytago:\\
A{B^2} + A{C^2} = B{C^2}\\
\Rightarrow A{C^2} = 7,{5^2} - 4,{5^2} = 36\\
\Rightarrow AC = 6\left( {cm} \right)\\
\Rightarrow AD + DC = 6\left( {cm} \right)\\
Theo\,t/c:\\
\frac{{AD}}{{AB}} = \frac{{DC}}{{BC}} = \frac{{AD + DC}}{{AB + BC}}\\
\Rightarrow \frac{{AD}}{{4,5}} = \frac{{DC}}{{7,5}} = \frac{6}{{4,5 + 7,5}} = \frac{6}{{12}} = \frac{1}{2}\\
\Rightarrow \left\{ \begin{array}{l}
AD = 2,25\left( {cm} \right)\\
DC = 3,75\left( {cm} \right)
\end{array} \right.\\
+ \Delta ABK = \Delta HBK\left( {ch - gn} \right)\\
\Rightarrow BH = AB = 4,5cm\\
\Rightarrow CH = BC - BH = 7,5 - 4,5 = 3\left( {cm} \right)\\
Và:AK = KH\\
\Rightarrow \frac{{KH}}{{AH}} = \frac{1}{2}\\
\frac{{AD}}{{DC}} = \frac{{2,75}}{{3,75}} = \frac{{11}}{{15}}\\
\Rightarrow \frac{{AD}}{{DC}} \ne \frac{{KH}}{{AH}}
\end{array}$
