Gọi O là trung điểm IK \(\Rightarrow OI=OK=\dfrac{1}{2}IK\)

\(\left(\overrightarrow{MI}+\overrightarrow{IA}\right)\left(\overrightarrow{MI}+\overrightarrow{IB}\right)+\left(\overrightarrow{MK}+\overrightarrow{KC}\right)\left(\overrightarrow{MK}+\overrightarrow{KD}\right)=\dfrac{1}{2}Ik^2\)

\(\Leftrightarrow MI^2-IA^2+MK^2-KC^2=\dfrac{1}{2}IK^2\)

\(\Leftrightarrow\left(\overrightarrow{MO}+\overrightarrow{OI}\right)^2+\left(\overrightarrow{MO}+\overrightarrow{OK}\right)^2=IA^2+KC^2+\dfrac{1}{2}IK^2\)

\(\Leftrightarrow2MO^2+2OI^2=IA^2+KC^2+\dfrac{1}{2}IK^2\)

\(\Leftrightarrow2MO^2+\dfrac{1}{2}IK^2=IA^2+KC^2+\dfrac{1}{2}IK^2\)

\(\Leftrightarrow MO^2=\dfrac{1}{2}\left(IA^2+KC^2\right)=\dfrac{1}{8}\left(AB^2+CD^2\right)\)

\(\Leftrightarrow MO=\dfrac{1}{2\sqrt{2}}\sqrt{AB^2+CD^2}\)

Tập hợp M là đường tròn tâm O bán kính \(\dfrac{\sqrt{AB^2+CD^2}}{2\sqrt{2}}\)

ko đọc đc chữ

a: BH=4,8cm

\(CuO\) + \(H_2\)→ \(Cu\) + \(H_2O\)

\(O_2\) + \(2H_2\)   → \(2H_2O\)

\(PbO\) + \(H_2\) → \(H_2O\) + \(Pb\)

\(Fe_2O_3\) + \(3H_2\) → \(2Fe\) + \(3H_2O\)

\(Fe_3O_4\) + \(4H_2\) →  \(3Fe\) + \(4H_2O\)

\(HgO\) + \(H_2\) → \(Hg\) + \(H_2O\)