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Argentina Contests
Argentina National Olympiad
2019 Argentina National Olympiad
3
3
Part of
2019 Argentina National Olympiad
Problems
(1)
<BAC = 3 <BAP wanted, <ACB = 2<ABC, AP = AC, PB = PC given
Source: 2019 Argentina OMA L3 p3
6/19/2020
In triangle
A
B
C
ABC
A
BC
it is known that
∠
A
C
B
=
2
∠
A
B
C
\angle ACB = 2\angle ABC
∠
A
CB
=
2∠
A
BC
. Furthermore
P
P
P
is an interior point of the triangle
A
B
C
ABC
A
BC
such that
A
P
=
A
C
AP = AC
A
P
=
A
C
and
P
B
=
P
C
PB = PC
PB
=
PC
. Prove that
∠
B
A
C
=
3
∠
B
A
P
\angle BAC = 3 \angle BAP
∠
B
A
C
=
3∠
B
A
P
.
geometry
angles
equal segments