MathDB
Problems
Contests
National and Regional Contests
China Contests
XES Mathematics Olympiad
the 15th XMO
1
1
Part of
the 15th XMO
Problems
(1)
Boring geometry proving by angle chasing in XMO
Source: 15th XMO
4/30/2024
A quadrilateral
A
B
C
D
ABCD
A
BC
D
with
A
B
⊥
B
C
AB \perp BC
A
B
⊥
BC
,
A
D
⊥
D
C
AD \perp DC
A
D
⊥
D
C
,
E
E
E
is a point that is on the line
B
D
BD
B
D
with
E
C
=
C
A
EC=CA
EC
=
C
A
,
F
F
F
,
G
G
G
is on the line
A
B
AB
A
B
A
D
AD
A
D
such that
E
F
⊥
A
C
EF\perp AC
EF
⊥
A
C
and
E
G
⊥
A
C
EG\perp AC
EG
⊥
A
C
,let
X
Y
X Y
X
Y
be the midpoint of segment
A
F
A
G
AF AG
A
F
A
G
, let
Z
W
Z W
Z
W
be the midpoint of segment
B
E
D
E
BE DE
BE
D
E
, try to proof that
(
W
B
X
)
(WBX)
(
W
BX
)
is tangent to
(
Z
D
Y
)
(ZDY)
(
Z
D
Y
)
geometry