If the vertices of a triangle obtained by joining the middle points of triangle ABC are (0,0),(2,0) and (1,root 3) then find vertices of triangle ABC and determine ratio of its sides

Question

If the vertices of a triangle obtained by joining the middle points of triangle ABC are (0,0),(2,0) and (1,root 3) then find vertices of triangle ABC and determine ratio  of its sides

aravindg · Answer

help pls

accessdenied · Answer

Sorry, this one I had to think about for a moment -- I graphed it and finally got the intuition of what to do.

The easiest way, I think, to go about this problem would be creating a system of equations for each side of ABC (and we can do that) and solving each combination of equations (we'll have three, so we will pair up all three into three groups.
The medial triangle (the one whose vertices we know) has sides that are parallel to the opposite sides of the triangle it is inscribed into.

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^ this would be a general case of a medial triangle inside of the triangle it is of