Question 106
In a triangle $ABC$, $A'$ is the foot of the height relative to the vertex $A$, and $H$ is the orthocenter.
a) Given a positive real number $k = \frac{AA'}{HA'}$, find the relationship between the angles $B$ and $C$ as a function of $k$.
b) If $B$ and $C$ are fixed, find the vertex locus $A$ for each value of $k$.
a) Given a positive real number $k = \frac{AA'}{HA'}$, find the relationship between the angles $B$ and $C$ as a function of $k$.
b) If $B$ and $C$ are fixed, find the vertex locus $A$ for each value of $k$.