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Chile National Olympiad
2023 Chile National Olympiad
6
6
Part of
2023 Chile National Olympiad
Problems
(1)
angle bisector wanted, 135-30-15 triangle
Source: 2023 Chile NMO L2 P6
5/19/2024
Let
△
A
B
C
\vartriangle ABC
△
A
BC
be a triangle such that
∠
A
B
C
=
3
0
o
\angle ABC = 30^o
∠
A
BC
=
3
0
o
,
∠
A
C
B
=
1
5
o
\angle ACB = 15^o
∠
A
CB
=
1
5
o
. Let
M
M
M
be midpoint of segment
B
C
BC
BC
and point
N
N
N
lies on segment
M
C
MC
MC
, such that the length of
N
C
NC
NC
is equal to length of
A
B
AB
A
B
. Proce that
A
N
AN
A
N
is the bisector of the angle
∠
M
A
C
\angle MAC
∠
M
A
C
. https://cdn.artofproblemsolving.com/attachments/2/7/4c554b53f03288ee69931fdd2c6fbd3e27ab13.png
geometry
angle bisector