MathDB
Problems
Contests
International Contests
APMO
2021 APMO
3
3
Part of
2021 APMO
Problems
(1)
Collinear Centers and Midarcs
Source: 2021 APMO P3
6/9/2021
Let
A
B
C
D
ABCD
A
BC
D
be a cyclic convex quadrilateral and
Γ
\Gamma
Γ
be its circumcircle. Let
E
E
E
be the intersection of the diagonals of
A
C
AC
A
C
and
B
D
BD
B
D
. Let
L
L
L
be the center of the circle tangent to sides
A
B
AB
A
B
,
B
C
BC
BC
, and
C
D
CD
C
D
, and let
M
M
M
be the midpoint of the arc
B
C
BC
BC
of
Γ
\Gamma
Γ
not containing
A
A
A
and
D
D
D
. Prove that the excenter of triangle
B
C
E
BCE
BCE
opposite
E
E
E
lies on the line
L
M
LM
L
M
.
geometry
circumcircle
APMO