Problem 2:
$\triangle ABC$ is a scalene triangle. $D$ is the midpoint of $BC$. $\triangle ADC$ is equilateral and $\triangle ADB$ is isosceles. Find the angles of $\triangle ABC$.
BdMO National Junior 2011/2
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
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sakibtanvir
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Re: BdMO National Junior 2011/2
In the triangle $ABC$ , $AD=DC=AC$ so,angle $ADC=60$ then angle $ADB=120$ if there is any other vertice equals to $BD$ then there there are total of the angles of triangle ABD greater than 180.so $AD=BD$.Now we can find those angels easily.which are 30,60 & 90.
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samiul_samin
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Re: BdMO National Junior 2011/2
Diagramsakibtanvir wrote: ↑Thu Jan 26, 2012 3:31 pmIn the triangle $ABC$ , $AD=DC=AC$ so,angle $ADC=60$ then $\angle {ADB}=120^{\circ}$ if there is any other vertice equals to $BD$ then there there are total of the angles of triangle ABD greater than $180^{\circ}$.so $AD=BD$.Now we can find those angels easily.which are $30^{\circ},60^{\circ}, 90^{\circ}.$