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China Contests
China National Olympiad
2020 China National Olympiad
2
2
Part of
2020 China National Olympiad
Problems
(1)
China Mathematical Olympiad 2020 Q2
Source: China Mathematical Olympiad 2020 Q2
11/26/2019
In triangle
A
B
C
ABC
A
BC
,
A
B
>
A
C
.
AB>AC.
A
B
>
A
C
.
The bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
meets
B
C
BC
BC
at
D
.
D.
D
.
P
P
P
is on line
D
A
,
DA,
D
A
,
such that
A
A
A
lies between
P
P
P
and
D
D
D
.
P
Q
PQ
PQ
is tangent to
⊙
(
A
B
D
)
\odot(ABD)
⊙
(
A
B
D
)
at
Q
.
Q.
Q
.
P
R
PR
PR
is tangent to
⊙
(
A
C
D
)
\odot(ACD)
⊙
(
A
C
D
)
at
R
.
R.
R
.
C
Q
CQ
CQ
meets
B
R
BR
BR
at
K
.
K.
K
.
The line parallel to
B
C
BC
BC
and passing through
K
K
K
meets
Q
D
,
A
D
,
R
D
QD,AD,RD
Q
D
,
A
D
,
R
D
at
E
,
L
,
F
,
E,L,F,
E
,
L
,
F
,
respectively. Prove that
E
L
=
K
F
.
EL=KF.
E
L
=
K
F
.
geometry