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National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Juniors 2003+ geometry
2004.8.7
2004.8.7
Part of
Kyiv City MO Juniors 2003+ geometry
Problems
(1)
angles in isosceles wanted, AM=2ВК, 24^o (Kyiv City Olympiad 2004 8.7 )
Source:
6/27/2021
In an isosceles triangle
A
B
C
ABC
A
BC
with base
A
C
AC
A
C
, on side
B
C
BC
BC
is selected point
K
K
K
so that
∠
B
A
K
=
2
4
o
\angle BAK = 24^o
∠
B
A
K
=
2
4
o
. On the segment
A
K
AK
A
K
the point
M
M
M
is chosen so that
∠
A
B
M
=
9
0
o
\angle ABM = 90^o
∠
A
BM
=
9
0
o
,
A
M
=
2
B
K
AM=2BK
A
M
=
2
B
K
. Find the values of all angles of triangle
A
B
C
ABC
A
BC
.
angles
geometry
isosceles