MathDB
Problems
Contests
National and Regional Contests
Azerbaijan Contests
Azerbaijan IZHO TST
2018 Azerbaijan IZhO TST
5
5
Part of
2018 Azerbaijan IZhO TST
Problems
(1)
Angle chasing I believe...
Source: Unknown
12/1/2019
Let
ω
\omega
ω
be the incircle of
△
A
B
C
\triangle ABC
△
A
BC
and
D
,
E
,
F
D,E,F
D
,
E
,
F
be the tangency points on
B
C
,
C
A
,
A
B
BC ,CA, AB
BC
,
C
A
,
A
B
. In
△
D
E
F
\triangle DEF
△
D
EF
let the altitudes from
E
,
F
E,F
E
,
F
to
F
D
,
D
E
FD,DE
F
D
,
D
E
intersect
A
B
,
A
C
AB, AC
A
B
,
A
C
at
X
,
Y
X ,Y
X
,
Y
. Prove that the second intersection of
(
A
E
X
)
(AEX)
(
A
EX
)
and
(
A
F
Y
)
(AFY)
(
A
F
Y
)
lies on
ω
\omega
ω
geometry
TST