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Problems
Contests
National and Regional Contests
China Contests
(China) National High School Mathematics League
1999 China Second Round Olympiad
1
1
Part of
1999 China Second Round Olympiad
Problems
(1)
1999 China Second Round Geometry
Source: 1999 China Second Round Olympiad P1
8/28/2019
In convex quadrilateral
A
B
C
D
,
∠
B
A
C
=
∠
C
A
D
.
ABCD, \angle BAC=\angle CAD.
A
BC
D
,
∠
B
A
C
=
∠
C
A
D
.
E
E
E
lies on segment
C
D
CD
C
D
, and
B
E
BE
BE
and
A
C
AC
A
C
intersect at
F
,
F,
F
,
D
F
DF
D
F
and
B
C
BC
BC
intersect at
G
.
G.
G
.
Prove that
∠
G
A
C
=
∠
E
A
C
.
\angle GAC=\angle EAC.
∠
G
A
C
=
∠
E
A
C
.
geometry