Three pins

Three pins stand between two plates of glass, and a soap film pulls itself as short as it can while joining them. Drag any pin: the film does not run along the sides of the triangle the pins make but meets at a point P in the middle, where its three pieces make 120° with one another. As long as three pieces meet at P, the three angles in the corner stay at 120.0°, and the film is shorter than the two shortest sides of the triangle put together. Drag a pin until the triangle's angle there reaches 120°, and P merges into that pin: the film is just two pieces, exactly those two sides. Bring that pin back and show Torricelli's construction: an equilateral triangle raised outward on each side, and their three circumcircles all pass through one point, which is P.