MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2018 Latvia Baltic Way TST
P10
P10
Part of
2018 Latvia Baltic Way TST
Problems
(1)
Obtuse triangle with symmetric points
Source: 2018 Latvia BW TST P10
3/26/2022
Let
A
B
C
ABC
A
BC
be an obtuse triangle with obtuse angle
∠
B
\angle B
∠
B
and altitudes
A
D
,
B
E
,
C
F
AD, BE, CF
A
D
,
BE
,
CF
. Let
T
T
T
and
S
S
S
be the midpoints of
A
D
AD
A
D
and
C
F
CF
CF
, respectively. Let
M
M
M
and
N
N
N
and be the symmetric images of
T
T
T
with respect to lines
B
E
BE
BE
and
B
D
BD
B
D
, respectively. Prove that
S
S
S
lies on the circumcircle of triangle
B
M
N
BMN
BMN
.
geometry
circumcircle