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National and Regional Contests
Bosnia Herzegovina Contests
JBMO TST - Bosnia and Herzegovina
2006 Bosnia and Herzegovina Junior BMO TST
2
2
Part of
2006 Bosnia and Herzegovina Junior BMO TST
Problems
(1)
equilateral wanted, <C=60^o, altitudes and midpoint
Source: 2006 Bosnia & Herzegovina JBMO TST p2
5/27/2020
In an acute triangle
A
B
C
ABC
A
BC
,
∠
C
=
6
0
o
\angle C = 60^o
∠
C
=
6
0
o
. If
A
A
′
AA'
A
A
′
and
B
B
′
BB'
B
B
′
are two of the altitudes and
C
1
C_1
C
1
is the midpoint of
A
B
AB
A
B
, prove that triangle
C
1
A
′
B
′
C_1A'B'
C
1
A
′
B
′
is equilateral.
geometry
Equilateral
altitude