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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2021 Sharygin Geometry Olympiad
8
8
Part of
2021 Sharygin Geometry Olympiad
Problems
(1)
Prove that two angles are equal in an isosceles triangle
Source: XVII Sharygin Correspondence Round P8
3/2/2021
Let
A
B
C
ABC
A
BC
be an isosceles triangle (
A
B
=
B
C
AB=BC
A
B
=
BC
) and
ℓ
\ell
ℓ
be a ray from
B
B
B
. Points
P
P
P
and
Q
Q
Q
of
ℓ
\ell
ℓ
lie inside the triangle in such a way that
∠
B
A
P
=
∠
Q
C
A
\angle BAP=\angle QCA
∠
B
A
P
=
∠
QC
A
. Prove that
∠
P
A
Q
=
∠
P
C
Q
\angle PAQ=\angle PCQ
∠
P
A
Q
=
∠
PCQ
.
geometry