MathDB
Problems
Contests
National and Regional Contests
Bulgaria Contests
Bulgaria EGMO TST
2021 Bulgaria EGMO TST
2021 Bulgaria EGMO TST
Part of
Bulgaria EGMO TST
Subcontests
(2)
1
1
Hide problems
Absolutely sad bruh geometry
On the side
A
B
AB
A
B
of a triangle
A
B
C
ABC
A
BC
is chosen a point
P
P
P
. Let
Q
Q
Q
be the midpoint of
B
C
BC
BC
and let
C
P
CP
CP
and
A
Q
AQ
A
Q
intersect at
R
R
R
. If
A
B
+
A
P
=
C
P
AB + AP = CP
A
B
+
A
P
=
CP
, prove that
C
R
=
A
B
CR = AB
CR
=
A
B
.
4
1
Hide problems
Intersecting diagonals in an n-gon
In a convex
n
n
n
-gon, several diagonals are drawn. Among these diagonals, a diagonal is called good if it intersects exactly one other diagonal drawn (in the interior of the
n
n
n
-gon). Find the maximum number of good diagonals.