This applet depicts Fermat Point. The Fermat Point is the point in a triangle where the distance to each point is the smallest combined value. In this applet, the Fermat Point is point H. The most common way used to find the Fermat Point is by making an equilateral triangle on two of the three sides or all three with the side length varying based on the length of the side the triangle is made on. After you get those triangles you make a line from the point opposite the side of the original triangle and make a line from that point to the opposite point in the original triangle (ex. line CE). Once at least two of those lines are made, they will intersect at the Fermat Point. Please move around the blue points (the original triangle) and experiment with how the Fermat Point moves.
1) Can the Fermat Point ever be outside of the original triangle? 2) Can two of the lines intersect in one place without the third? 3) Does the Fermat Point tend to be near the smallest side, middle-sized side, or largest side? Why do you think this is?