[/quote]
,
that satisfy the equation
with incenter 
.
at 
.
and 
be points on the side BC such that 
and 
,
and 
be the incenter of triangles 
and 
,
is the Euler line of triangle 
.
,
,
,
,
are odd primes and![\[2^ap^b=(p+2)^c-1.\]](http://latex.artofproblemsolving.com/5/8/5/58518a8ebed14836b72af743ff100eae2efba5e2.png)
we have 
.
.
be reals such that 
and 
Prove that
is the reflection of 
the intersection of 
is the reflection of 
.
be the reflection of 
.
concyclic.
. Prove that: 
at 
and ray 
at 
. The circumcircle of triangle 
intersects the circumcircle 
of triangle 
distinct from point 
and 
intersect 
and 
respectively.
such that 
for all real number 
and 
is an equilateral . Let 
and 
at 
and 
at 
,
on 
satisfies 
and 
.
be the point where the perpendicular from 
to line 
meets the angle bisector of 
.
holds.
be a positive integer such that 
.
.
Y by
Let 
be a trapezoid such that 
. Two circles 
and 
are located inside the trapezoid so that is tangent to 
and is tangent to 
. Let 
be a line passing through 
, other than 
, tangent to . Let 
be a line passing through 
, other than 
, tangent to . Show that 
.
be a trapezoid such that 
. Two circles 
and 
are located inside the trapezoid so that is tangent to 
and is tangent to 
. Let 
be a line passing through 
, other than 
, tangent to . Let 
be a line passing through 
, other than 
, tangent to . Show that 
.This post has been edited 1 time. Last edited by parmenides51, Sep 27, 2020, 6:17 AM
