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Korea Junior Mathematics Olympiad
2014 Korea Junior Math Olympiad
1
1
Part of
2014 Korea Junior Math Olympiad
Problems
(1)
concyclic Points
Source: 2014 Korea Junior Olympiad Round 2 #1
9/29/2016
Given
△
A
B
C
\triangle ABC
△
A
BC
with incenter
I
I
I
. Line
A
I
AI
A
I
meets
B
C
BC
BC
at
D
D
D
. The incenter of
△
A
B
D
,
△
A
D
C
\triangle ABD, \triangle ADC
△
A
B
D
,
△
A
D
C
are
E
,
F
E,F
E
,
F
, respectively. Line
D
E
DE
D
E
meets the circumcircle of
△
B
C
E
\triangle BCE
△
BCE
at
P
(
≠
E
)
P(\neq E)
P
(
=
E
)
and line
D
F
DF
D
F
meets the circumcircle of
△
B
C
F
\triangle BCF
△
BCF
at
Q
(
≠
F
)
Q(\neq F)
Q
(
=
F
)
. Show that the midpoint of
B
C
BC
BC
lies on the circumcircle of
△
D
P
Q
\triangle DPQ
△
D
PQ
.
geometry