,
,
define 
to be the semiperimeter of 
.
be a triangle and let 
be on side 
such that![\[\frac{s(ABD)}{BD}=\frac{s(ACD)}{CD}\]](http://latex.artofproblemsolving.com/9/4/f/94f0bcb2cf847452d6e6197d5bb9b6f0ffd72f6d.png)
Let 
be a point on 
.
and 
be on 
and 
such that 
and 
.
parallel to 
and 
intersect 
,
,
and circumcentre 
.
be the midpoint of 
is a parallellogram. Suppose that there exists a point 
to 
.
.
,
.
such that:
Y by Mango247
Let 
be a triangle with 
are midpoints of 
respectively. The circle 
of center 
has a big enough radius cuts 
at 
. Define circles 
with 
similarly. Suppose that these circles have the same radius, prove that 
are concyclic.
be a triangle with 
are midpoints of 
respectively. The circle 
of center 
has a big enough radius cuts 
at 
. Define circles 
with 
similarly. Suppose that these circles have the same radius, prove that 
are concyclic.This post has been edited 2 times. Last edited by parmenides51, Sep 12, 2020, 11:26 PM
