geo problem triangle
Geometry
Level
pending
the area of triangle ABC is 1. BD<DA, DG//BC, DE//AC, GF//AB, solve the maximum area of DGFE. Round your answer to the thousands.
ps, the point on the left is E and the one on the right is F
The answer is 0.333.
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1 solution
If D divides AB in the ratio k:1 i.e. AD/DB =k with k>1 then we need to maximize the expression: 1 - k^2/(k+1)^2 -2/(k+1)^2. (I leave it to the reader to work out why this is so). It can be readily ascertained that at k=2 this expression is maximum at 1/3.