[tex]\it AB||CD \Rightarrow m(\stackrel\frown{DA})=m(\stackrel\frown{BC})\\ \\ \{m(\stackrel\frown{AB}),\ \ m(\stackrel\frown{BC}),\ \ m(\stackrel\frown{CD})\}\ d.\ p.\ \{6,\ \ 5,\ \ 8\} \Rightarrow\begin{cases}\ \it m(\stackrel\frown{AB})=6k\\ \\ \it m(\stackrel\frown{BC})=5k\\ \\ \it m(\stackrel\frown{CD})=8k\end{cases}\\ \\ \\ m(\stackrel\frown{DA})=m(\stackrel\frown{BC})=5k[/tex]
[tex]\it 6k+5k+8k+5k=360^o \Rightarrow 24k=360^o|_{:24} \Rightarrow k=15^o \Rightarrow \\ \\ \Rightarrow m(\stackrel\frown{AB})=6\cdot15^o=90^o;\ \ \ m(\stackrel\frown{CD})=8\cdot15^o=120^o[/tex]
[tex]\it m(\widehat{AOB})=m(\stackrel\frown{AB})=90^o \Rightarrow \Delta AOB-dreptunghic\ isoscel, OA=OB=4\ cm,\\ \\ BC=4\sqrt2\ cm;\ \ \ d(O,\ \ AB)=\dfrac{OA\cdot OB}{AB}=\dfrac{4\cdot4}{4\sqrt2}=\dfrac{4}{\sqrt2}=\dfrac{4\sqrt2}{2}=2\sqrt2\ cm[/tex]
[tex]\it m(\widehat{COD})=m(\stackrel\frown{CD})=120^o \Rightarrow m(\widehat{OCD})=m(\widehat{ODC})=30^o\\ \\ Th.\ \angle30^o \Rightarrow d(O,\ \ CD)=OC:2=4:2=2\ cm[/tex]
