\[\boxed{\mathbf{574.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[\mathrm{\Delta}ABC.\]
\[\mathbf{Доказать:}\]
\[\textbf{а)}\ h = \frac{\text{ab}}{c};\]
\[\textbf{б)}\frac{a^{2}}{a_{c}} = \frac{b^{2}}{b_{c}}.\]
\[\mathbf{Доказательство.}\]
\[\textbf{а)}\ S_{\text{ABC}} = \frac{1}{2}\text{ab\ }и\ S_{\text{ABC}} = \frac{1}{2}ch:\]
\[ab = ch\]
\[\ h = \frac{\text{ab}}{c}.\]
\[Что\ и\ требовалось\ доказать.\]
\[\textbf{б)}\ a = \sqrt{a_{c} \bullet c}\]
\[a^{2} = a_{c} \bullet c\]
\[\ c = \frac{a^{2}}{a_{c}}.\]
\[b = \sqrt{b_{c} \bullet c}\]
\[b^{2} = b_{c} \bullet c\]
\[\ c = \frac{b^{2}}{\text{bc}}.\]
\[Получаем:\ \]
\[\frac{a^{2}}{a_{c}} = \frac{b^{2}}{b_{c}}.\]
\[Что\ и\ требовалось\ доказать.\]