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Contests & Programs
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First Poster
Last Poster
force overlay inversion vibes
v4913 63
N
Yesterday at 1:47 PM
by starchan
Source: USAMO 2023/6
Let
be a triangle with incenter
and excenters
,
, and
opposite
,
, and
, respectively. Let
be an arbitrary point on the circumcircle of
that does not lie on any of the lines
,
, or
. Suppose the circumcircles of
and
intersect at two distinct points
and
. If
is the intersection of lines
and
, prove that
.
Proposed by Zach Chroman





















Proposed by Zach Chroman
63 replies
Is EGMO good for JMO Geometry Questions?
MathRook7817 4
N
Tuesday at 2:10 PM
by MathRook7817
Hi guys, I was just wondering if EGMO is a good book for JMO/AMO/olympiad level questions, or if there exists another olympiad geo book. Thanks!
4 replies
Question about AMC 10
MathNerdRabbit103 15
N
May 5, 2025
by GallopingUnicorn45
Hi,
Can anybody predict a good score that I can get on the AMC 10 this November by only being good at counting and probability, number theory, and algebra? I know some geometry because I took it in school though, but it isn’t competition math so it probably doesn’t count.
Thanks.
Can anybody predict a good score that I can get on the AMC 10 this November by only being good at counting and probability, number theory, and algebra? I know some geometry because I took it in school though, but it isn’t competition math so it probably doesn’t count.
Thanks.
15 replies
Find the radius of circle O
TheMaskedMagician 3
N
May 4, 2025
by fruitmonster97
Source: 1976 AHSME Problem 18
IMAGE
In the adjoining figure,
is tangent at
to the circle with center
; point
is interior to the circle; and
intersects the circle at
. If
,
, and
, then the radius of the circle is
In the adjoining figure,










3 replies
Tangent Circles in the Coordinate Plane
inventivedant 24
N
May 4, 2025
by lpieleanu
Source: 2022 AMC 10B #22 / 2022 AMC 12B #21
Let
be the set of circles in the coordinate plane that are tangent to each of the three circles with equations
,
, and
. What is the sum of the areas of all circles in
?






24 replies
System
worthawholebean 10
N
Apr 29, 2025
by daijobu
Source: AIME 2008II Problem 14
Let
and
be positive real numbers with
. Let
be the maximum possible value of
for which the system of equations
has a solution in
satisfying
and
. Then
can be expressed as a fraction
, where
and
are relatively prime positive integers. Find
.





![\[ a^2+y^2=b^2+x^2=(a-x)^2+(b-y)^2\]](http://latex.artofproblemsolving.com/1/3/4/13432a7d6e5c1465e08d513ee64c6c7ce99d75f9.png)








10 replies
Angel Bisector and Equilateral Pentagon AMNPQ
El_Ectric 46
N
Apr 29, 2025
by pikapika007
Source: 2016 USAMO 5
An equilateral pentagon
is inscribed in triangle
such that
,
, and
. Let
be the intersection of
and
. Denote by
the angle bisector of
.
Prove that
is parallel to
, where
is the circumcenter of triangle
, and
is the incenter of triangle
.










Prove that






46 replies
USAJMO #5 - points on a circle
hrithikguy 208
N
Apr 28, 2025
by Adywastaken
Points
lie on a circle
and point
lies outside the circle. The given points are such that (i) lines
and
are tangent to
, (ii)
are collinear, and (iii)
. Prove that
bisects
.










208 replies
Complex numbers in geometry
v_Enhance 34
N
Apr 28, 2025
by ESAOPS
Source: 2012 AIME I Problem 14
Complex numbers
,
and
are the zeros of a polynomial
, and
. The points corresponding to
,
, and
in the complex plane are the vertices of a right triangle with hypotenuse
. Find
.










34 replies
Two Pentagons
r00tsOfUnity 54
N
Apr 27, 2025
by ESAOPS
Source: 2023 AMC 10B #25 / 2023 AMC 12B #25
A regular pentagon with area
is printed on paper and cut out. The five vertices of the pentagon are folded into the center of the pentagon, creating a smaller pentagon. What is the area of the new pentagon?


54 replies
