Question

Va rog sa ma ajutati: Fie triunghiul ABC cu m ( A ) = 90 , , AD perpendicular BC , D€ BC .Aratati : 1/ AD² = 1/ AB²+ 1/AC₂

Answer 1

$\frac{1}{ AD^{2} } = \frac{1}{ (\frac{AB*AC}{BC})^{2} } = \frac{ BC^{2} }{ AB^{2}* AC^{2} } = \frac{ AB^{2}+ AC^{2} }{ AB^{2}* AC^{2} }= \frac{ AB^{2} }{ AB^{2}* AC^{2} }+ \frac{ AC^{2} }{ AB^{2}* AC^{2} }= \\ \\ = \frac{1}{ AC^{2} } + \frac{1}{ AB^{2} } .$