MathDB
Problems
Contests
National and Regional Contests
Peru Contests
Peru Cono Sur TST
2020 Peru Cono Sur TST.
P3
P3
Part of
2020 Peru Cono Sur TST.
Problems
(1)
BM angle bisector of <TBC wanted
Source: 2020 Peru Ibero + Cono Sur TST p3
11/27/2021
Let
A
B
C
ABC
A
BC
be an acute triangle with
∣
A
B
∣
>
∣
A
C
∣
| AB | > | AC |
∣
A
B
∣
>
∣
A
C
∣
. Let
D
D
D
be the foot of the altitude from
A
A
A
to
B
C
BC
BC
, let
K
K
K
be the intersection of
A
D
AD
A
D
with the internal bisector of angle
B
B
B
, Let
M
M
M
be the foot of the perpendicular from
B
B
B
to
C
K
CK
C
K
(it could be in the extension of segment
C
K
CK
C
K
) and
N
N
N
the intersection of
B
M
BM
BM
and
A
K
AK
A
K
(it could be in the extension of the segments). Let
T
T
T
be the intersection of
A
C
AC
A
C
with the line that passes through
N
N
N
and parallel to
D
M
DM
D
M
. Prove that
B
M
BM
BM
is the internal bisector of the angle
∠
T
B
C
\angle TBC
∠
TBC
geometry
angle bisector