Problem 2.1: In what kind of triangle is the orthocenter also the circumcircle? [Solution]

Problem 2.2: In what kind of triangle is the centroid also the incircle? [Solution]

Problem 2.3: What does it say about a triangle if one of its sides is also an altitude [Solution]

Problem 2.4: What must be true of a triangle if its circumcenter lies in the interior of the triangle? [Solution]

Problem 2.5: If segments AD and BF are medians of triangle ABC, how long is segment AD? [Solution]