Question 2
In the interiors of the sides $AB$, $BC$, $CA$ of a given triangle $ABC$, points $K$, $L$ and $M$, respectively, are given such that
$$
\frac{|AK|}{|KB|} = \frac{|BL|}{|LC|} = \frac{|CM|}{|MA|}
$$
Show that the triangles $ABC$ and $KLM$ have a common orthocenter if and only if the triangle $ABC$ is equilateral.
$$
\frac{|AK|}{|KB|} = \frac{|BL|}{|LC|} = \frac{|CM|}{|MA|}
$$
Show that the triangles $ABC$ and $KLM$ have a common orthocenter if and only if the triangle $ABC$ is equilateral.