(Originais Teachy 2023) - Question Hard of Mathematics

Consider a board game where players move pieces along straight line segments drawn on the board. In the game, there are two pieces A and B allocated at different points on the board. To achieve victory, a player must move their piece along the straight line segment that connects the points where pieces A and B are located. Pieces A and B are in places that form a straight line with a third point C, which is also on the board. Players must answer the following questions to advance in the game: 1) If a player can move their piece along a straight line segment connecting pieces A and B, what can we say about the relative position of the line segments formed by points A, B, and C? 2) If the line segments formed by points A, B, and C are concurrent, how can we classify the relative position of the lines passing through A and C and through B and C? Justify your answers based on the concepts of lines, segments, and rays.