cute geo
by Royal_mhyasd, May 28, 2025, 7:54 AM
Let 
be an acute triangle and 
it's incenter. Let 
, 
and 
be the projections of onto 
, 
and 
respectively. 
and 
is the projection of onto 
. Let 
be the middle of the arc not containing 
and 
the second intersection of 
and the circumcircle of 
. If 
is the midpoint of 
, 
, 
and 
, prove that 
is cyclic.
PS i'm not sure if this problem is actually original so if it isn't someone please tell me so i can change the source (if that's possible)
be an acute triangle and 
it's incenter. Let 
, 
and 
be the projections of onto 
, 
and 
respectively. 
and 
is the projection of onto 
. Let 
be the middle of the arc not containing 
and 
the second intersection of 
and the circumcircle of 
. If 
is the midpoint of 
, 
, 
and 
, prove that 
is cyclic.PS i'm not sure if this problem is actually original so if it isn't someone please tell me so i can change the source (if that's possible)
and 
such that 
.
,
be an even integer and let 
be real numbers satisfying 
.
such that
has a solution
be an arbitrary set. Then a collection 
of subsets of 
for each 
the set 
for every finite sequence 
of elements each 
the union 
algebra on 
of elements each 
,
be an infinite set. And let 
is finite. Prove that 
then 
to 
be such a function.
)
be the union 
then 
is an infinite set. Thus, 
is countable.
and 
be different points on a circle 
such that 
is not a diameter. Let 
be the tangent line to 
.
is chosen on the shorter arc 
of triangle 
intersects 
meets 
is tangent to 
April 2021
February 2021