Matt has build an additional support for his hut (\(AD\)), whose length is equal to the height of the hut calculated in the Example 1. What are the distances from the base of the support to both ends of the hut? Looking at the picture, what are the distances \(BD\) and \(DC\), if \(AB = 20\) and \(AC = 15\)? Show that \(AD^2 = BD \times AC\) in this particular case. Do you think it is true in general?