MathDB
Problems
Contests
International Contests
Iranian Geometry Olympiad
2014 Iran Geometry Olympiad (senior)
3:
3:
Part of
2014 Iran Geometry Olympiad (senior)
Problems
(1)
Iranian geometry olympiad 2014(4)
Source: Iranian geometry olympiad 2014
2/25/2015
Let
A
B
C
ABC
A
BC
be an acute triangle.A circle with diameter
B
C
BC
BC
meets
A
B
AB
A
B
and
A
C
AC
A
C
at
E
E
E
and
F
F
F
,respectively.
M
M
M
is midpoint of
B
C
BC
BC
and
P
P
P
is point of intersection
A
M
AM
A
M
with
E
F
EF
EF
.
X
X
X
is an arbitary point on arc
E
F
EF
EF
and
Y
Y
Y
is the second intersection of
X
P
XP
XP
with a circle with diameter
B
C
BC
BC
.Prove that
∡
X
A
Y
=
∡
X
Y
M
\measuredangle XAY=\measuredangle XYM
∡
X
A
Y
=
∡
X
Y
M
. Author:Ali zo'alam , Iran
geometry
Iran