MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2020 Latvia Baltic Way TST
11
11
Part of
2020 Latvia Baltic Way TST
Problems
(1)
Brocard's theorem FTW
Source: Latvia TST for Baltic Way 2020 P11
10/18/2020
Circle centred at point
O
O
O
intersects sides
A
C
,
A
B
AC, AB
A
C
,
A
B
of triangle
△
A
B
C
\triangle ABC
△
A
BC
at points
B
1
B_1
B
1
and
C
1
C_1
C
1
respectively and passes through points
B
,
C
B,C
B
,
C
. It is known that lines
A
O
,
C
C
1
,
B
B
1
AO, CC_1, BB_1
A
O
,
C
C
1
,
B
B
1
are concurrent. Prove that
△
A
B
C
\triangle ABC
△
A
BC
is isosceles.
geometry
FTW