Question

Answer 1

hình e tự vẽ 

có: DM=DA

\(\Rightarrow DM=DC=DE\\ \Rightarrow MD=\dfrac{1}{2}EC\\ \Rightarrow\Delta EMCvgtạiM\)

(vì trung tuyến MD=1/2EC)

\(\Rightarrow\Delta EMC\sim\Delta ECB\left(gg\right)\)( tự xét)

b) có \(\Delta EMC\sim\Delta ECB\Rightarrow\dfrac{EM}{EC}=\dfrac{CB}{MC}\)

\(\Rightarrow EM.MC=CB.EC=a.2a=2a^2\)

c) có: \(S_{EBC}=\dfrac{1}{2}.EC.BC=\dfrac{1}{2}.2a.a=a^2\\ EB=\sqrt{EC^2+BC^2}=\sqrt{\left(2a\right)^2+a^2}=\sqrt{5}a\\ \Delta EMC\sim\Delta ECB\)

\(\Rightarrow\dfrac{S_{EMC}}{S_{EBC}}=\left(\dfrac{EC}{EB}\right)^2=\left(\dfrac{2a}{\sqrt{5}a}\right)^2=\dfrac{4}{5}\\ \Rightarrow S_{EMC}=\dfrac{4}{5}a^2\)