MathDB
Problems
Contests
National and Regional Contests
China Contests
(China) National High School Mathematics League
2022 China Second Round
1
China Second Round MO Test 2 P1
China Second Round MO Test 2 P1
Source:
September 11, 2022
chang 09
Problem Statement
In a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
,
∠
A
B
C
=
∠
A
D
C
=
9
0
∘
\angle ABC = \angle ADC = 90^\circ
∠
A
BC
=
∠
A
D
C
=
9
0
∘
. A point
P
P
P
is chosen from the diagonal
B
D
BD
B
D
such that
∠
A
P
B
=
2
∠
C
P
D
\angle APB = 2\angle CPD
∠
A
PB
=
2∠
CP
D
, points
X
X
X
,
Y
Y
Y
is chosen from the segment
A
P
AP
A
P
such that
∠
A
X
B
=
2
∠
A
D
B
\angle AXB = 2\angle ADB
∠
A
XB
=
2∠
A
D
B
,
∠
A
Y
D
=
2
∠
A
B
D
\angle AYD = 2\angle ABD
∠
A
Y
D
=
2∠
A
B
D
. Prove that:
B
D
=
2
X
Y
BD = 2XY
B
D
=
2
X
Y
.
Back to Problems
View on AoPS