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National and Regional Contests
Turkey Contests
Turkey EGMO TST
2019 Turkey EGMO TST
3
3
Part of
2019 Turkey EGMO TST
Problems
(1)
Turkey EGMO TST 2019 P3
Source: Turkey EGMO TST 2019
3/15/2019
Let
ω
\omega
ω
be the circumcircle of
Δ
A
B
C
\Delta ABC
Δ
A
BC
, where
∣
A
B
∣
=
∣
A
C
∣
|AB|=|AC|
∣
A
B
∣
=
∣
A
C
∣
. Let
D
D
D
be any point on the minor arc
A
C
AC
A
C
. Let
E
E
E
be the reflection of point
B
B
B
in line
A
D
AD
A
D
. Let
F
F
F
be the intersection of
ω
\omega
ω
and line
B
E
BE
BE
and Let
K
K
K
be the intersection of line
A
C
AC
A
C
and the tangent at
F
F
F
. If line
A
B
AB
A
B
intersects line
F
D
FD
F
D
at
L
L
L
, Show that
K
,
L
,
E
K,L,E
K
,
L
,
E
are collinear points
geometry