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ABC is an isosceles triangle with angle A = 120 degrees.  If G is the centroid of the triangle, and AD is the median, then find BG/DG.

 May 19, 2020
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See the following image  :

 

 

Let    B  =(-sqrt (3) , 0)   A  = (0, 1)   C = ( sqrt (3), 0  )

 

The  centroid occurs at the intersection of the medians = G

 

Let BE  be  the median drawn to  AC

 

cot (EBC)  =    (sqrt (3)  + sqrt (3)/2 )   / (1/2)     =  [ 3sqrt (3) / 2]  / (1/2)  = 3sqrt(3) =  BD/DG

 

cool cool cool

 May 19, 2020

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