MathDB
Problems
Contests
National and Regional Contests
Peru Contests
Peru Cono Sur TST
2003 Peru Cono Sur TST
P3
P3
Part of
2003 Peru Cono Sur TST
Problems
(1)
Spiral center?
Source: 2003 Peru Cono Sur TST P3
5/3/2023
Let
M
M
M
and
N
N
N
be points on the side
B
C
BC
BC
of a triangle
A
B
C
ABC
A
BC
such that
B
M
=
C
N
BM = CN
BM
=
CN
(
M
M
M
lies between
B
B
B
and
N
N
N
). Points
P
P
P
and
Q
Q
Q
lie on
A
N
AN
A
N
and
A
M
AM
A
M
respectively, so that
∠
P
M
C
=
∠
M
A
B
\angle PMC =\angle MAB
∠
PMC
=
∠
M
A
B
and
∠
Q
N
B
=
∠
N
A
C
\angle QNB = \angle NAC
∠
QNB
=
∠
N
A
C
. Prove that
∠
Q
B
C
=
∠
P
C
B
\angle QBC = \angle PCB
∠
QBC
=
∠
PCB
.
geometry