cho a-b/b-c = c-d/d-a chứng minh a=c hoặc a+c= b+d
$ \frac{a - b}{b - c} = \frac{c - d}{d - a} \\\Rightarrow ad - bd - a^2 + ab = bc - c^2 - bd + cd \\\Leftrightarrow ad + ab - bc - bd + c^2 - a^2 + bd - bd = 0 \\\Leftrightarrow -a(-b - d) + c(-b - d) + (c - a)(c + a) = 0 \\\Leftrightarrow (-b - d) (c - a) + (c - a) (c + a) = 0 \\\Leftrightarrow (c - a) (c + a - b - d) = 0 \\\Leftrightarrow
\left\{\begin{matrix}
c - a = 0\\
c + a - b - d = 0
\end{matrix}\right. \\\Leftrightarrow
\left\{\begin{matrix}
c = a\\
c + a = b + d
\end{matrix}\right. $