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Iran Team Selection Test
2022 Iran Team Selection Test
3
3
Part of
2022 Iran Team Selection Test
Problems
(1)
Iran TST P3
Source: Iranian TST 2022 problem 3
4/2/2022
Incircle
ω
\omega
ω
of triangle
A
B
C
ABC
A
BC
is tangent to sides
C
B
CB
CB
and
C
A
CA
C
A
at
D
D
D
and
E
E
E
, respectively. Point
X
X
X
is the reflection of
D
D
D
with respect to
B
B
B
. Suppose that the line
D
E
DE
D
E
is tangent to the
A
A
A
-excircle at
Z
Z
Z
. Let the circumcircle of triangle
X
Z
E
XZE
XZE
intersect
ω
\omega
ω
for the second time at
K
K
K
. Prove that the intersection of
B
K
BK
B
K
and
A
Z
AZ
A
Z
lies on
ω
\omega
ω
.Proposed by Mahdi Etesamifard and Alireza Dadgarnia
geometry