Hình học Oxy

X

xuanquynh97

$AB:y−2=0 ; BC: x\sqrt{3}−y+2=0$ \Rightarrow $B(0;2)$

$AB:y−2=0$ \Rightarrow $AB//Ox$ $AC \bot Ox$ \Rightarrow $x_A=x_C$

Đặt $x_A=x_C=m$ \Rightarrow $A(m;2);C(m;m\sqrt{3}+2)$

\Rightarrow $AB=|m|;AC=|m\sqrt{3}|;BC=|2m|$

$2S_{ABC}=AB.AC=(AB+BC+AC).r$ \Rightarrow $m^2\sqrt{3}=|3m+m\sqrt{3}|.3$

\Rightarrow $m^4=3(3m+m\sqrt{3})^2$ \Rightarrow $m^2=3(3+\sqrt{3})2$

\Rightarrow $m_1=3(\sqrt{3}+1)$ và $m_2=−3(\sqrt{3}+1)$
 
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