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Find tha maximum value
sqing 2
N
by sqing
Source: China Zhejiang High School Mathematics Competition 2025 Q7
Let 
be reals such that 
Find tha maximum value of 
be reals such that 
Find tha maximum value of 
2 replies
Find tha minimum value
sqing 3
N
by sqing
Source: China Zhejiang High School Mathematics Competition 2025 Q6
Let 
be reals such that 
and 
Find tha minimum value of 
be reals such that 
and 
Find tha minimum value of 
3 replies
CSMGO P6: Incenter lies on radax of two interesting circles
amar_04 13
N
by WLOGQED1729
Source: https://artofproblemsolving.com/community/c594864h2372843p19407517
Let 
be a triangle with the incenter 
, and let the incircle 
of touch 
at points 
respectively. Let 
intersect again at a point 
. Let the lines through 
and 
parallel to 
intersect again at points 
respectively. Prove that lies on the common chord of the circumcircle of 
and the circumcircle of 
.
be a triangle with the incenter 
, and let the incircle 
of touch 
at points 
respectively. Let 
intersect again at a point 
. Let the lines through 
and 
parallel to 
intersect again at points 
respectively. Prove that lies on the common chord of the circumcircle of 
and the circumcircle of 
.
13 replies
Beijing High School Mathematics Competition 2025 Q1
SunnyEvan 2
N
by SunnyEvan
Let 
. Prove that:
. Prove that:
2 replies
Prove that
Lord Evan the Reflector
whatshisbucket 24
N
by Trasher_Cheeser12321
Source: ELMO 2018 #3, 2018 ELMO SL G3
Let 
be a point in the plane, and 
a line not passing through . Evan does not have a straightedge, but instead has a special compass which has the ability to draw a circle through three distinct noncollinear points. (The center of the circle is not marked in this process.) Additionally, Evan can mark the intersections between two objects drawn, and can mark an arbitrary point on a given object or on the plane.
(i) Can Evan construct* the reflection of over ?
(ii) Can Evan construct the foot of the altitude from to ?
*To construct a point, Evan must have an algorithm which marks the point in finitely many steps.
Proposed by Zack Chroman
be a point in the plane, and 
a line not passing through . Evan does not have a straightedge, but instead has a special compass which has the ability to draw a circle through three distinct noncollinear points. (The center of the circle is not marked in this process.) Additionally, Evan can mark the intersections between two objects drawn, and can mark an arbitrary point on a given object or on the plane.(i) Can Evan construct* the reflection of
over ?(ii) Can Evan construct the foot of the altitude from
to ?*To construct a point, Evan must have an algorithm which marks the point in finitely many steps.
Proposed by Zack Chroman
24 replies
Expanding tan z?
ys-lg 0
How to expand 
by residue theorem? Should by something like
![\[[z^n]\tan z\propto\oint _{|z|=N}\frac{\tan z}{z^{n+1}}\mathrm dz\]](//latex.artofproblemsolving.com/8/5/c/85c34140e3cc61d93bd3188c22ae06649ca98c5a.png)
where 
tends to infty, but I'm not sure about details.
by residue theorem? Should by something like![\[[z^n]\tan z\propto\oint _{|z|=N}\frac{\tan z}{z^{n+1}}\mathrm dz\]](http://latex.artofproblemsolving.com/8/5/c/85c34140e3cc61d93bd3188c22ae06649ca98c5a.png)
where 
tends to infty, but I'm not sure about details.
0 replies
Iran second round 2025-q1
mohsen 7
N
by Mathgloggers
Find all positive integers n>2 such that sum of n and any of its prime divisors is a perfect square.
7 replies
Show that 
.![$$ \frac{ a}{b}+\frac{b}{c}+\frac{c}{a}\geq \sqrt[3]{49}$$](http://latex.artofproblemsolving.com/4/1/7/41747f09ab60b8e1a07de01f23d11985133c0d17.png)
.
Double integration
Tricky123 1
N
by greenturtle3141
Q)
![\[\iint_{R} \sin(xy) \,dx\,dy, \quad R = \left[0, \frac{\pi}{2}\right] \times \left[0, \frac{\pi}{2}\right]\]](//latex.artofproblemsolving.com/a/2/0/a205868dd99f4794de53ad1db50f34b17c70a923.png)
How to solve the problem like this I am using the substitution method but its seems like very complicated in the last
Please help me
![\[\iint_{R} \sin(xy) \,dx\,dy, \quad R = \left[0, \frac{\pi}{2}\right] \times \left[0, \frac{\pi}{2}\right]\]](http://latex.artofproblemsolving.com/a/2/0/a205868dd99f4794de53ad1db50f34b17c70a923.png)
How to solve the problem like this I am using the substitution method but its seems like very complicated in the last
Please help me
1 reply
