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KoMaL A Problems
KoMaL A Problems 2022/2023
A. 845
A. 845
Part of
KoMaL A Problems 2022/2023
Problems
(1)
Circles through vertices tangent to the incircle
Source: KoMaL A. 845
3/11/2023
The incircle of triangle
A
B
C
ABC
A
BC
is tangent to sides
B
C
BC
BC
,
A
C
AC
A
C
, and
A
B
AB
A
B
at points
D
D
D
,
E
E
E
and
F
F
F
, respectively. Let
A
′
A'
A
′
denote the point of the incircle for which circle
(
A
′
B
C
)
(A'BC)
(
A
′
BC
)
is tangent to the incircle. Define points
B
′
B'
B
′
and
C
′
C'
C
′
similarly. Prove that lines
A
′
D
A'D
A
′
D
,
B
E
′
BE'
B
E
′
, and
C
F
′
CF'
C
F
′
are concurrent.Proposed by Áron Bán-Szabó, Budapest
geometry
komal