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National and Regional Contests
Russia Contests
Novosibirsk Oral Olympiad in Geometry
2021 Novosibirsk Oral Olympiad in Geometry
6
6
Part of
2021 Novosibirsk Oral Olympiad in Geometry
Problems
(1)
AQ=BP if AP=PQ=QC, <PBQ = 30^o, equilateral (2021 Novosibirsk Oral Geo Oly 7.6)
Source:
4/27/2021
Inside the equilateral triangle
A
B
C
ABC
A
BC
, points
P
P
P
and
Q
Q
Q
are chosen so that the quadrilateral
A
P
Q
C
APQC
A
PQC
is convex,
A
P
=
P
Q
=
Q
C
AP = PQ = QC
A
P
=
PQ
=
QC
and
∠
P
B
Q
=
3
0
o
\angle PBQ = 30^o
∠
PBQ
=
3
0
o
. Prove that
A
Q
=
B
P
AQ = BP
A
Q
=
BP
.
geometry
equal segments
Equilateral