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Tournament Of Towns
1994 Tournament Of Towns
(410) 1
(410) 1
Part of
1994 Tournament Of Towns
Problems
(1)
3 points coincide, symmetric of antidiametric wrt midpoint is fixed
Source: TOT 410 1994 Spring O S1 - Tournament of Towns
6/12/2024
A triangle
A
B
C
ABC
A
BC
is inscribed in a circle. Let
A
1
A_1
A
1
be the point diametrically opposed to
A
A
A
,
A
0
A_0
A
0
be the midpoint of the side
B
C
BC
BC
and
A
2
A_2
A
2
be the point symmetric to
A
1
A_1
A
1
with respect to
A
0
A_0
A
0
; the points
B
2
B_2
B
2
and
C
2
C_2
C
2
are defined in a similar way starting from
B
B
B
and
C
C
C
. Prove that the three points
A
2
A_2
A
2
,
B
2
B_2
B
2
and
C
2
C_2
C
2
coincide.(A Jagubjanz)
geometry
symmetry