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International Contests
International Olympiad of Metropolises
2018 IOM
6
6
Part of
2018 IOM
Problems
(1)
Point P on incircle with <APE = <DPB
Source: IOM 2018 #6, Dušan Djukić
9/6/2018
The incircle of a triangle
A
B
C
ABC
A
BC
touches the sides
B
C
BC
BC
and
A
C
AC
A
C
at points
D
D
D
and
E
E
E
, respectively. Suppose
P
P
P
is the point on the shorter arc
D
E
DE
D
E
of the incircle such that
∠
A
P
E
=
∠
D
P
B
\angle APE = \angle DPB
∠
A
PE
=
∠
D
PB
. The segments
A
P
AP
A
P
and
B
P
BP
BP
meet the segment
D
E
DE
D
E
at points
K
K
K
and
L
L
L
, respectively. Prove that
2
K
L
=
D
E
2KL = DE
2
K
L
=
D
E
.Dušan Djukić
geometry
incircle