Question 61
Let $ABC$ be a triangle with medians $m_{a}, m_{b}, m_{c}$. Prove that:
a. There is a triangle with side lengths $m_{a}, m_{b}, m_{c}$.
b. This triangle is similar to $ABC$ if and only if the squares of the side lengths of triangle $ABC$ form an arithmetical sequence.
a. There is a triangle with side lengths $m_{a}, m_{b}, m_{c}$.
b. This triangle is similar to $ABC$ if and only if the squares of the side lengths of triangle $ABC$ form an arithmetical sequence.