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Last Poster
Arc Midpoints Form Cyclic Quadrilateral
ike.chen 57
N
an hour ago
by cj13609517288
Source: ISL 2022/G2
In the acute-angled triangle
, the point
is the foot of the altitude from
, and
is a point on the segment
. The lines through
parallel to
and
meet
at
and
, respectively. Points
and
lie on the circles
and
, respectively, such that
and
.
Prove that
and
are concyclic.

















Prove that


57 replies
1 viewing
Complex number
ronitdeb 0
an hour ago
Let
be vertices of regular pentagon inscribed in a circle whose radius is
and center is at
. Find all possible values of




0 replies
Elementary Problems Compilation
Saucepan_man02 29
N
an hour ago
by Electrodynamix777
Could anyone send some elementary problems, which have tricky and short elegant methods to solve?
For example like this one:
Solve over reals:
For example like this one:
Solve over reals:

29 replies
Generic Real-valued FE
lucas3617 4
N
2 hours ago
by GreekIdiot




4 replies

Find all possible values of BT/BM
va2010 54
N
2 hours ago
by lpieleanu
Source: 2015 ISL G4
Let
be an acute triangle and let
be the midpoint of
. A circle
passing through
and
meets the sides
and
at points
and
respectively. Let
be the point such that
is a parallelogram. Suppose that
lies on the circumcircle of
. Determine all possible values of
.















54 replies
A Familiar Point
v4913 52
N
2 hours ago
by SimplisticFormulas
Source: EGMO 2023/6
Let
be a triangle with circumcircle
. Let
and
respectively denote the midpoints of the arcs
and
that do not contain the third vertex. Let
denote the midpoint of arc
(the arc
including
). Let
be the incenter of
. Let
be the circle that is tangent to
and internally tangent to
at
, and let
be the circle that is tangent to
and internally tangent to
at
. Show that the line
, and the lines through the intersections of
and
, meet on
.
























52 replies
Tangential quadrilateral and 8 lengths
popcorn1 72
N
2 hours ago
by cj13609517288
Source: IMO 2021 P4
Let
be a circle with centre
, and
a convex quadrilateral such that each of the segments
and
is tangent to
. Let
be the circumcircle of the triangle
. The extension of
beyond
meets
at
, and the extension of
beyond
meets
at
. The extensions of
and
beyond
meet
at
and
, respectively. Prove that ![\[A D+D T+T X+X A=C D+D Y+Y Z+Z C.\]](//latex.artofproblemsolving.com/8/2/6/8261276053071cc6cc06dda824a883426bf1d4ac.png)
Proposed by Dominik Burek, Poland and Tomasz Ciesla, Poland






















![\[A D+D T+T X+X A=C D+D Y+Y Z+Z C.\]](http://latex.artofproblemsolving.com/8/2/6/8261276053071cc6cc06dda824a883426bf1d4ac.png)
Proposed by Dominik Burek, Poland and Tomasz Ciesla, Poland
72 replies
An algorithm for discovering prime numbers?
Lukaluce 3
N
2 hours ago
by TopGbulliedU
Source: 2025 Junior Macedonian Mathematical Olympiad P3
Is there an infinite sequence of prime numbers
such that for every
is satisfied? Explain the answer.


3 replies
Random concyclicity in a square config
Maths_VC 5
N
2 hours ago
by Royal_mhyasd
Source: Serbia JBMO TST 2025, Problem 1
Let
be a random point on the smaller arc
of the circumcircle of square
, and let
be the intersection point of segments
and
. The feet of the tangents from point
to the circumcircle of the triangle
are
and
, where
is the center of the square. Prove that points
,
,
and
lie on a single circle.















5 replies
Basic ideas in junior diophantine equations
Maths_VC 3
N
3 hours ago
by Royal_mhyasd
Source: Serbia JBMO TST 2025, Problem 3
Determine all positive integers
and
such that





3 replies
