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MathLinks Contest 5th
6.1
6.1
Part of
MathLinks Contest 5th
Problems
(1)
0561 geometry 5th edition Round 6 p1
Source:
5/6/2021
Let
A
B
C
ABC
A
BC
be a triangle and let
C
C
C
be a circle that intersects the sides
B
C
,
C
A
BC, CA
BC
,
C
A
and
A
B
AB
A
B
in the points
A
1
,
A
2
,
B
1
,
B
2
A_1, A_2, B_1, B_2
A
1
,
A
2
,
B
1
,
B
2
and
C
1
,
C
2
C_1, C_2
C
1
,
C
2
respectively. Prove that if
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
are concurrent lines then
A
A
2
,
B
B
2
AA_2, BB_2
A
A
2
,
B
B
2
and
C
C
2
CC_2
C
C
2
are also concurrent lines.
geometry
5th edition