CM tiếp tuyến hộ mình

D

doanhnhanvanhoa

C

congchuaanhsang

Kẻ OI vuông góc với FG

Đặt AB=BC=CD=DA=a

$\Delta$ADG $\sim$ $\Delta$FBK \Rightarrow $\dfrac{AD}{FB}$=$\dfrac{DG}{BK}$

\RightarrowDG=$\dfrac{AD}{FB}.BK$=$\dfrac{a}{ \dfrac{3}{4}a }.\dfrac{a}{2}$=$\dfrac{2a}{3}$

\RightarrowCG=$\dfrac{a}{3}$ ; MG=$\dfrac{a}{2}-\dfrac{a}{3}=\dfrac{a}{6}$

$GF^2=CF^2+CG^2$=$\dfrac{25a^2}{144}$

\RightarrowGF=$\dfrac{5a}{12}$

$S_{OGF}$=$S_{OMCN}$-$(S_{ONF}+S_{OMG}+S_{CGF})$=$\dfrac{5a^2}{48}$

Mặt khác $S_{OGF}$=$\dfrac{1}{2}OI.GF$=$OI.\dfrac{5a}{12}$

\RightarrowOI=$\dfrac{a}{2}$\Rightarrowđpcm
 
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