Question 56
Triangle $ABC$ has $\hat{B}, \hat{C} \lt 90^\circ$ and $AB \neq AC$. Denote $m, n, p$ the measures of the angles made by the altitude, the bisector, respectively the median from $A$ with $BC$. Show that the angle $\hat{A}$ is right if and only if $n$ is the arithmetic mean of $m$ and $p$.
Claudiu Ştefan Popa
Claudiu Ştefan Popa