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National and Regional Contests
China Contests
XES Mathematics Olympiad
the 11th XMO
1
1
Part of
the 11th XMO
Problems
(1)
Geometry in XMO, don't discuss until tomorrow
Source: 11th XMO Test 2 P1
2/13/2023
Let
△
A
B
C
\triangle ABC
△
A
BC
be connected to the circle
Γ
\Gamma
Γ
. The angular bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
intersects
B
C
BC
BC
to
D
D
D
. Straight line
B
P
BP
BP
intersects
A
C
AC
A
C
to
E
E
E
, and straight line
C
P
CP
CP
intersects
A
B
AB
A
B
to
F
F
F
. Let the tangent of the circle
Γ
\Gamma
Γ
at point
A
A
A
intersect the line
E
F
EF
EF
at the point
Q
Q
Q
. Proof:
P
Q
∥
B
C
PQ\parallel BC
PQ
∥
BC
.
geometry
xmo