MathDB
Problems
Contests
National and Regional Contests
Bosnia Herzegovina Contests
JBMO TST - Bosnia and Herzegovina
2020 Bosnia and Herzegovina Junior BMO TST
3
3
Part of
2020 Bosnia and Herzegovina Junior BMO TST
Problems
(1)
JBMO TST Bosnia and Herzegovina 2020 P3
Source:
8/10/2020
The angle bisector of
∠
A
B
C
\angle ABC
∠
A
BC
of triangle
A
B
C
ABC
A
BC
(
A
B
>
B
C
AB>BC
A
B
>
BC
) cuts the circumcircle of that triangle in
K
K
K
. The foot of the perpendicular from
K
K
K
to
A
B
AB
A
B
is
N
N
N
, and
P
P
P
is the midpoint of
B
N
BN
BN
. The line through
P
P
P
parallel to
B
C
BC
BC
cuts line
B
K
BK
B
K
in
T
T
T
. Prove that the line
N
T
NT
NT
passes through the midpoint of
A
C
AC
A
C
.
geometry
angle bisector