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National and Regional Contests
Moldova Contests
Moldova Team Selection Test
1995 Moldova Team Selection Test
3
3
Part of
1995 Moldova Team Selection Test
Problems
(1)
the circumcircles of $BCB_1, CAC_1$ and $ABA_1$ are congruent
Source: Moldova TST 1995
8/8/2023
Let
A
B
C
ABC
A
BC
be a triangle with the medians
A
A
1
,
B
B
1
AA_1, BB_1
A
A
1
,
B
B
1
and
C
C
1
CC_1{}
C
C
1
. Prove that if the circumcircles of
B
C
B
1
,
C
A
C
1
BCB_1, CAC_1
BC
B
1
,
C
A
C
1
and
A
B
A
1
ABA_1
A
B
A
1
are congruent then
A
B
C
ABC
A
BC
is equilateral.
geometry
circumcircle