Matt has built an additional support for his hut (\(AD\)), whose length is \(12\)ft, and the base \(BC\) is \(25\)ft. We also know \(AB = 20\) and \(AC = 15\). What are the distances \(|BD|\) and \(|DC|\)? Show that \(|AD|^2=|BD| \times |AC|\) in this particular case. Do you think it is true in general?