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KoMaL A Problems
KoMaL A Problems 2020/2021
A. 796
A. 796
Part of
KoMaL A Problems 2020/2021
Problems
(1)
Nice Geometry
Source: KöMaL A. 796
3/24/2022
Let
A
B
C
D
ABCD
A
BC
D
be a cyclic quadrilateral. Let lines
A
B
AB
A
B
and
C
D
CD
C
D
intersect in
P
,
P,
P
,
and lines
B
C
BC
BC
and
D
A
DA
D
A
intersect in
Q
.
Q.
Q
.
The feet of the perpendiculars from
P
P
P
to
B
C
BC
BC
and
D
A
DA
D
A
are
K
K
K
and
L
,
L,
L
,
and the feet of the perpendiculars from
Q
Q
Q
to
A
B
AB
A
B
and
C
D
CD
C
D
are
M
M
M
and
N
.
N.
N
.
The midpoint of diagonal
A
C
AC
A
C
is
F
.
F.
F
.
Prove that the circumcircles of triangles
F
K
N
FKN
F
K
N
and
F
L
M
,
FLM,
F
L
M
,
and the line
P
Q
PQ
PQ
are concurrent.Based on a problem by Ádám Péter Balogh, Szeged
geometry
komal