functions such that
for all real numbers 
and 
with equal radii are given. Let 
and 
are on 
,
and 
.
as the other intersection of 
and 
.
are concurrent.
such that 
days later (but perhaps earlier, as well). Hedvig received the trophy today. Determine all integers 
for which we can be absolutely certain that she cannot receive the trophy again in 
days, given the above information.
Y by
Let 
be a cyclic quadrilateral and let 
be the intersection of its diagonals. Let 
and 
be the midpoints of 
and 
, respectively, and let 
be the orthocenter of triangle 
. Let 
on line and 
on line such that 
. If 
is the circumcenter of , show that 
.
be a cyclic quadrilateral and let 
be the intersection of its diagonals. Let 
and 
be the midpoints of 
and 
, respectively, and let 
be the orthocenter of triangle 
. Let 
on line and 
on line such that 
. If 
is the circumcenter of , show that 
.This post has been edited 1 time. Last edited by parmenides51, Dec 4, 2021, 6:47 PM
