MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
Turkey Team Selection Test
2019 Turkey Team SeIection Test
3
3
Part of
2019 Turkey Team SeIection Test
Problems
(1)
Bisector and altitude relations
Source: Turkey TST 2019 Day 1 P3
3/26/2019
In a triangle
A
B
C
ABC
A
BC
,
A
B
>
A
C
AB>AC
A
B
>
A
C
. The foot of the altitude from
A
A
A
to
B
C
BC
BC
is
D
D
D
, the intersection of bisector of
B
B
B
and
A
D
AD
A
D
is
K
K
K
, the foot of the altitude from
B
B
B
to
C
K
CK
C
K
is
M
M
M
and let
B
M
BM
BM
and
A
K
AK
A
K
intersect at point
N
N
N
. The line through
N
N
N
parallel to
D
M
DM
D
M
intersects
A
C
AC
A
C
at
T
T
T
. Prove that
B
M
BM
BM
is the bisector of angle
T
B
C
^
\widehat{TBC}
TBC
.
geometry