Problem : In what kind of triangle is the orthocenter also the circumcircle?An equilateral triangle
Problem : In what kind of triangle is the centroid also the incircle?An equilateral triangle
Problem : What does it say about a triangle if one of its sides is also an altitudeThe triangle is a right triangle.
Problem : What must be true of a triangle if its circumcenter lies in the interior of the triangle?The triangle must be acute.
Problem : If segments AD and BF are medians of triangle ABC, how long is segment AD?