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In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

 Jun 13, 2024
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What is DE ?

 

\(\overline{BC}^2=\overline{AB}^2+\overline{AC}^2-2\cdot \overline{AB}\cdot \overline{AC}\cdot cos\ \alpha\\ \alpha =acos\ ( \dfrac{\overline{AB}^2+\overline{AC}^2-\overline{BC}^2}{2\cdot \overline{AB}\cdot \overline{AC}})\\ \alpha =acos\ (\dfrac{13^2+19^2-3^2}{2\cdot 13\cdot 19})=acos\ (1.0546\ ...)\\ \alpha =\ unreal\)

 

The segments 3, 13 and 19 do not form a closed triangle.

laugh !

 Jun 14, 2024
edited by asinus  Jun 14, 2024
edited by asinus  Jun 14, 2024
edited by asinus  Jun 14, 2024

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