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National and Regional Contests
Argentina Contests
Argentina National Olympiad
2011 Argentina National Olympiad
3
3
Part of
2011 Argentina National Olympiad
Problems
(1)
computational staring with w 90-57-15 triangle, <APB =<CPQ, <BQA=<CQP
Source: 2011 Argentina OMA L3 p3
6/17/2020
Let
A
B
C
ABC
A
BC
be a triangle with
∠
A
=
9
0
o
,
∠
B
=
7
5
o
\angle A = 90^o, \angle B = 75^o
∠
A
=
9
0
o
,
∠
B
=
7
5
o
and
A
B
=
2
AB = 2
A
B
=
2
. The points
P
P
P
and
Q
Q
Q
on the sides
A
C
AC
A
C
and
B
C
BC
BC
respectively are such that
∠
A
P
B
=
∠
C
P
Q
\angle APB = \angle CPQ
∠
A
PB
=
∠
CPQ
and
∠
B
Q
A
=
∠
C
Q
P
\angle BQA = \angle CQP
∠
BQ
A
=
∠
CQP
. Calculate the measurement of the segment
Q
A
QA
Q
A
.
geometry
equal angles
right triangle