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Contests
National and Regional Contests
North Macedonia Contests
JBMO TST - Macedonia
2017 Macedonia JBMO TST
4
4
Part of
2017 Macedonia JBMO TST
Problems
(1)
Show that BM + CM > AY [Macedonia JBMO TST 2017, P4]
Source: Macedonia JBMO TST 2017, Problem 4
6/26/2018
In triangle
A
B
C
ABC
A
BC
, the points
X
X
X
and
Y
Y
Y
are chosen on the arc
B
C
BC
BC
of the circumscribed circle of
A
B
C
ABC
A
BC
that doesn't contain
A
A
A
so that
∡
B
A
X
=
∡
C
A
Y
\measuredangle BAX = \measuredangle CAY
∡
B
A
X
=
∡
C
A
Y
. Let
M
M
M
be the midpoint of the segment
A
X
AX
A
X
. Show that
B
M
+
C
M
>
A
Y
.
BM + CM > AY.
BM
+
CM
>
A
Y
.
circumcircle
geometry
Geometric Inequalities