prove that sides of orthic triangle meet the sides of the given triangle in 3 colinear points

Question

$ABC$ is a triangle and $EFG$ is its orthic triangle. prove that sides of orthic triangle meet the sides of the triangle $ABC$ in 3 colinear points.

i drew the following figure..i just need an approach or a hint.

thankyou!

Answer 1

This actually follows directly from Desargue's theorem:

Given two arbitrary triangles $ABC$ and $EFG$, the lines $AG, \, BE$ and $CE$ are concurrent if and only if the three intersection points $R = CA \cap FG, \, S = BC \cap EF$ and $T = AB \cap GE$ are collinear.