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Problems
Contests
National and Regional Contests
Bolivia Contests
Bolivian Ibero TST
2021 Bolivia Ibero TST
4
4
Part of
2021 Bolivia Ibero TST
Problems
(1)
Why no normal geometry :(
Source: Bolivia Ibero TST 2021 Day 2 P2
9/2/2022
On a isosceles triangle
△
A
B
C
\triangle ABC
△
A
BC
with
A
B
=
B
C
AB=BC
A
B
=
BC
let
K
,
M
K,M
K
,
M
be the midpoints of
A
B
,
A
C
AB,AC
A
B
,
A
C
respectivily. Let
(
C
K
B
)
(CKB)
(
C
K
B
)
intersect
B
M
BM
BM
at
N
≠
M
N \ne M
N
=
M
, the line through
N
N
N
parallel to
A
C
AC
A
C
intersects
(
A
B
C
)
(ABC)
(
A
BC
)
at
A
1
,
C
1
A_1,C_1
A
1
,
C
1
. Show that
△
A
1
B
C
1
\triangle A_1BC_1
△
A
1
B
C
1
is equilateral.
geometry
Bolivia
TST
isosceles