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CMIMC Problems
2022 CMIMC
3
3
Part of
2022 CMIMC
Problems
(1)
2022 Team P3
Source:
2/28/2022
Let
A
B
C
D
ABCD
A
BC
D
be a rectangle with
A
B
=
10
AB=10
A
B
=
10
and
A
D
=
5.
AD=5.
A
D
=
5.
Suppose points
P
P
P
and
Q
Q
Q
are on segments
C
D
CD
C
D
and
B
C
,
BC,
BC
,
respectively, such that the following conditions hold:[*]
B
D
∥
P
Q
BD \parallel PQ
B
D
∥
PQ
[*]
∠
A
P
Q
=
9
0
∘
.
\angle APQ=90^{\circ}.
∠
A
PQ
=
9
0
∘
.
What is the area of
△
C
P
Q
?
\triangle CPQ?
△
CPQ
?
Proposed by Kyle Lee
team