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All-Russian Olympiad Regional Round
2010 All-Russian Olympiad Regional Round
9.4
9.4
Part of
2010 All-Russian Olympiad Regional Round
Problems
(1)
point symmetric of vertex wrt line connecting feet of bisectors lies on side
Source: Russian Regional Olympiad 2010 9.4
8/24/2024
In triangle
A
B
C
ABC
A
BC
,
∠
A
=
6
0
o
\angle A =60^o
∠
A
=
6
0
o
. Let
B
B
1
BB_1
B
B
1
and
C
C
1
CC_1
C
C
1
be angle bisectors of this triangle. Prove that the point symmetrical to vertex
A
A
A
with respect to line
B
1
C
1
B_1C_1
B
1
C
1
lies on side
B
C
BC
BC
.
geometry
symmetry