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MAA AMC
USAJMO
2021 USAJMO
2
2
Part of
2021 USAJMO
Problems
(1)
Erecting Rectangles
Source: 2021 USAMO Problem 1/2021 USAJMO Problem 2
4/15/2021
Rectangles
B
C
C
1
B
2
,
BCC_1B_2,
BC
C
1
B
2
,
C
A
A
1
C
2
,
CAA_1C_2,
C
A
A
1
C
2
,
and
A
B
B
1
A
2
ABB_1A_2
A
B
B
1
A
2
are erected outside an acute triangle
A
B
C
.
ABC.
A
BC
.
Suppose that
∠
B
C
1
C
+
∠
C
A
1
A
+
∠
A
B
1
B
=
18
0
∘
.
\angle BC_1C+\angle CA_1A+\angle AB_1B=180^{\circ}.
∠
B
C
1
C
+
∠
C
A
1
A
+
∠
A
B
1
B
=
18
0
∘
.
Prove that lines
B
1
C
2
,
B_1C_2,
B
1
C
2
,
C
1
A
2
,
C_1A_2,
C
1
A
2
,
and
A
1
B
2
A_1B_2
A
1
B
2
are concurrent.
AMC
USA(J)MO
USAMO
geometry
rectangle