MathDB
Problems
Contests
International Contests
KoMaL A Problems
KoMaL A Problems 2017/2018
A. 716
A. 716
Part of
KoMaL A Problems 2017/2018
Problems
(1)
OD perpendicular to BC
Source: KöMaL A. 716
3/14/2018
Let
A
B
C
ABC
A
BC
be a triangle and let
D
D
D
be a point in the interior of the triangle which lies on the angle bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
. Suppose that lines
B
D
BD
B
D
and
A
C
AC
A
C
meet at
E
E
E
, and that lines
C
D
CD
C
D
and
A
B
AB
A
B
meet at
F
F
F
. The circumcircle of
A
B
C
ABC
A
BC
intersects line
E
F
EF
EF
at points
P
P
P
and
Q
Q
Q
. Show that if
O
O
O
is the circumcenter of
D
P
Q
DPQ
D
PQ
, then
O
D
OD
O
D
is perpendicular to
B
C
BC
BC
.Michael Ren
geometry