Finding multiple paths to solve a task

The task: Show different ways to construct an equilateral triangle based on a given vertex C and one its side lying on a given line. A crucial stage to make sense of what the task involves is to problematize its statement. That is, to think of the task it in terms of questions in order to identify relevant information and comprehend what is asked. For instance, what data or information is provided? What does it mean that one side of the triangles lies on a given line? Where is the third vertex located? What properties does an equilateral triangle hold? The ned figure shows a point C as the given vertex and a line l. Then, the goal is where to locate segment AB on line l, so that triangle ABC is equilateral.