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Problems
Contests
National and Regional Contests
Iran Contests
Iran RMM TST
2020 Iran RMM TST
2
2
Part of
2020 Iran RMM TST
Problems
(1)
Circle in triangle
Source: 239 2014 S7
1/14/2020
A circle
ω
\omega
ω
is strictly inside triangle
A
B
C
ABC
A
BC
. The tangents from
A
A
A
to
ω
\omega
ω
intersect
B
C
BC
BC
in
A
1
,
A
2
A_1,A_2
A
1
,
A
2
define
B
1
,
B
2
,
C
1
,
C
2
B_1,B_2,C_1,C_2
B
1
,
B
2
,
C
1
,
C
2
similarly. Prove that if five of six points
A
1
,
A
2
,
B
1
,
B
2
,
C
1
,
C
2
A_1,A_2,B_1,B_2,C_1,C_2
A
1
,
A
2
,
B
1
,
B
2
,
C
1
,
C
2
lie on a circle the sixth one lie on the circle too.
geometry