Question 3
Let $ABC$ be a triangle with altitudes $AD,BE,CF$. Points $A',B',C'$ lie on $AD,BE,CF$, respectively, and satisfy
$$\frac{AA'}{AD}=\frac{BB'}{BE}=\frac{CC'}{CF}=k.$$
Determine all $k$ for which triangle $A'B'C'$ is similar to triangle $ABC$.
$$\frac{AA'}{AD}=\frac{BB'}{BE}=\frac{CC'}{CF}=k.$$
Determine all $k$ for which triangle $A'B'C'$ is similar to triangle $ABC$.