MathDB
Problems
Contests
National and Regional Contests
Canada Contests
Canada National Olympiad
1974 Canada National Olympiad
2
Rectangle
Rectangle
Source: Canada 1974/2
January 13, 2007
geometry
rectangle
trigonometry
parallelogram
Problem Statement
Let
A
B
C
D
ABCD
A
BC
D
be a rectangle with
B
C
=
3
A
B
BC=3AB
BC
=
3
A
B
. Show that if
P
,
Q
P,Q
P
,
Q
are the points on side
B
C
BC
BC
with
B
P
=
P
Q
=
Q
C
BP = PQ = QC
BP
=
PQ
=
QC
, then
∠
D
B
C
+
∠
D
P
C
=
∠
D
Q
C
.
\angle DBC+\angle DPC = \angle DQC.
∠
D
BC
+
∠
D
PC
=
∠
D
QC
.
Back to Problems
View on AoPS