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KoMaL A Problems
KoMaL A Problems 2022/2023
A. 840
A. 840
Part of
KoMaL A Problems 2022/2023
Problems
(1)
Classic incenter configurations again
Source: KoMaL A. 840
1/11/2023
The incircle of triangle
A
B
C
ABC
A
BC
touches the sides in
X
X
X
,
Y
Y
Y
and
Z
Z
Z
. In triangle
X
Y
Z
XYZ
X
Y
Z
the feet of the altitude from
X
X
X
and
Y
Y
Y
are
X
′
X'
X
′
and
Y
′
Y'
Y
′
, respectively. Let line
X
′
Y
′
X'Y'
X
′
Y
′
intersect the circumcircle of triangle
A
B
C
ABC
A
BC
at
P
P
P
and
Q
Q
Q
. Prove that points
X
X
X
,
Y
Y
Y
,
P
P
P
and
Q
Q
Q
are concyclic.Proposed by László Simon, Budapest
geometry
incenter
komal