MathDB
Problems
Contests
International Contests
CentroAmerican
2019 Centroamerican and Caribbean Math Olympiad
4
4
Part of
2019 Centroamerican and Caribbean Math Olympiad
Problems
(1)
2019 Central American and Caribbean Mathematical Olympiad, P4
Source:
6/19/2019
Let
A
B
C
ABC
A
BC
be a triangle,
Γ
\Gamma
Γ
its circumcircle and
l
l
l
the tangent to
Γ
\Gamma
Γ
through
A
A
A
. The altitudes from
B
B
B
and
C
C
C
are extended and meet
l
l
l
at
D
D
D
and
E
E
E
, respectively. The lines
D
C
DC
D
C
and
E
B
EB
EB
meet
Γ
\Gamma
Γ
again at
P
P
P
and
Q
Q
Q
, respectively. Show that the triangle
A
P
Q
APQ
A
PQ
is isosceles.
geometry
circumcircle