MathDB
Problems
Contests
International Contests
May Olympiad
May Olympiad L2 - geometry
May Olympiad L2 - geometry
Part of
May Olympiad
Subcontests
(1)
2012.3
1
Hide problems
Perpendiculars and Angle Bisectors
Given Triangle
A
B
C
ABC
A
BC
,
∠
B
=
2
∠
C
\angle B= 2 \angle C
∠
B
=
2∠
C
, and
∠
A
>
9
0
∘
\angle A>90^\circ
∠
A
>
9
0
∘
. Let
M
M
M
be midpoint of
B
C
BC
BC
. Perpendicular of
A
C
AC
A
C
at
C
C
C
intersects
A
B
AB
A
B
at
D
D
D
. Show
∠
A
M
B
=
∠
D
M
C
\angle AMB = \angle DMC
∠
A
MB
=
∠
D
MC
If possible, don't use projective geometry