and 
,
cookies from one of the piles, of which he eats 
and puts 
for which Marica has a winning strategy.
be non-negative real numbers such that 
Prove that
Y by Adventure10
In a triangle 
, let 
and 
be points of the sides 
and 
respectively. Segments 
and 
intersect at 
. Suppose that the line connecting midpoints of the triangle and parallel to 
, bisects the segment 
. Prove that the triangle 
and the quadrilateral 
have equal areas.
, let 
and 
be points of the sides 
and 
respectively. Segments 
and 
intersect at 
. Suppose that the line connecting midpoints of the triangle and parallel to 
, bisects the segment 
. Prove that the triangle 
and the quadrilateral 
have equal areas.This post has been edited 2 times. Last edited by parmenides51, Sep 24, 2021, 4:34 PM
Reason: latex
Reason: latex
midline, it is easy to get from the length of feet on ![\[[BAE]+[ABD]=[ABC].\]](http://latex.artofproblemsolving.com/b/2/4/b245669991858f0fcb96aff3b74da28c05eb5ace.png)
Thus we have ![\[2[AOB]+[DOB]+[EOA] = [ABC]=[CDOE]+[EOA]+[AOB]+[DOB]\implies [ABO]=[ODCE].\]](http://latex.artofproblemsolving.com/8/e/5/8e5edfe29f5fdc70dbaba4d3fede99ba267dd0d8.png)
