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Kharkiv City MO Seniors - geometry
2013.11.4
2013.11.4
Part of
Kharkiv City MO Seniors - geometry
Problems
(1)
<AA_ K=<BB_1M when B_1K//BC, A_1M//AC (Kharkiv City XI 2013 - Ukr)
Source:
3/13/2020
In the triangle
A
B
C
ABC
A
BC
, the heights
A
A
1
AA_1
A
A
1
and
B
B
1
BB_1
B
B
1
are drawn. On the side
A
B
AB
A
B
, points
M
M
M
and
K
K
K
are chosen so that
B
1
K
∥
B
C
B_1K\parallel BC
B
1
K
∥
BC
and
A
1
M
∥
A
C
A_1 M\parallel AC
A
1
M
∥
A
C
. Prove that the angle
A
A
1
K
AA_1K
A
A
1
K
is equal to the angle
B
B
1
M
BB_1M
B
B
1
M
.
geometry
parallel
equal angles
angles
Kharkiv