is given where 
are positive reals. Prove that:
be a triangle and let 
be a circle in its plane passing through 
and 
Suppose there exist circles 
such that for 
is externally tangent to 
and passes through 
and 
where 
for all 
.
and 
have common external tangents 
and 
meeting at 
.
and 
.
through 
and 
,
is convex.
and 
meet at point 
,
.
Y by Adventure10
Let 
be a point in the interior 
, and 
3 concurrent cevians through , with 
on 
. The circle with the diameter 
intersects the circle with the diameter 
in 
. Analogously we define 
and 
. Prove that 
are concylic.
be a point in the interior 
, and 
3 concurrent cevians through , with 
on 
. The circle with the diameter 
intersects the circle with the diameter 
in 
. Analogously we define 
and 
. Prove that 
are concylic.
