Oplossing week 23

q13703img1.gif

$
\eqalign{
  & \frac{1}
{{\sqrt 3 }} = \frac{{8 - x}}
{x}  \cr
  & x = \sqrt 3 \left( {8 - x} \right)  \cr
  & x^2  = 3\left( {8 - x} \right)^2   \cr
  & x^2  = 3\left( {64 - 16x + x^2 } \right)  \cr
  & x^2  = 192 - 48x + 3x^2   \cr
  & 2x^2  - 48x + 192 = 0  \cr
  & x^2  - 24x + 96 = 0  \cr
  & (x - 12)^2  - 48 = 0  \cr
  & x = 12 - 4\sqrt 3  \vee x = 12 + 4\sqrt 3 \,\,(v.n.)  \cr
  & x = 12 - 4\sqrt 3   \cr
  & O_{\Delta ABC}  = \frac{1}
{2} \cdot 8\left( {12 - 4\sqrt 3 } \right) = 48 - 16\sqrt 3  \cr}
$



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