a, xet \(\Delta AOB\) va \(\Delta COD\)
\(\widehat{AOB}=\widehat{DOC}\left(dd\right)\);\(\widehat{ODC}=\widehat{ABO}\)(sole trog)
\(\Rightarrow\Delta AOB\infty\Delta COD\left(gg\right)\)
\(\Rightarrow\dfrac{OA}{OC}=\dfrac{OB}{OD}\)
\(\Rightarrow\dfrac{OA}{OA+OC}=\dfrac{OB}{OB+OD}\)
\(\Rightarrow\dfrac{OA}{AC}=\dfrac{OB}{BD}\)
b, xet \(\Delta DOI\) va \(\Delta DBA\)
\(\widehat{D}chung\) ; \(\widehat{DIO}=\widehat{DAB}=90\)
\(\Delta DOI\infty\Delta DBA\) \(\Rightarrow\dfrac{DO}{BD}=\dfrac{OI}{AB}\left(2\right)\)
xet \(\Delta COE\) va \(\Delta CAB\)
\(\widehat{C}chung;\widehat{BAO}=\widehat{EOC}\)(AB//IE)
\(\Rightarrow\Delta COE\infty\Delta CAB\)\(\Rightarrow\dfrac{CO}{AC}=\dfrac{OE}{AB}\left(1\right)\)
Ta co:\(\dfrac{OA}{OC}=\dfrac{OB}{OD}\Rightarrow\dfrac{OC}{OA}=\dfrac{OD}{OB}\)
\(\Rightarrow\dfrac{OC}{OC+OA}=\dfrac{OD}{OD+OB}\)
\(\Rightarrow\dfrac{OC}{AC}=\dfrac{OD}{BD}\left(3\right)\)
Tu (1) (2) (3) \(\Rightarrow\dfrac{OI}{AB}=\dfrac{OE}{AB}\Rightarrow OI=OE\)
c,Ta co:\(\Delta AKD\infty\Delta ADC\left(gg\right)\)
\(\Delta DKC\infty\Delta ADC\left(gg\right)\)
\(\Rightarrow\Delta AKD\infty\Delta DKC\Rightarrow\dfrac{AK}{DK}=\dfrac{DK}{KC}\)
\(\Rightarrow DK^2=KC.AK=36\Rightarrow DK=6cm\)
câu c mấy cái tg đồng dạng kia bn tự c/m nha
