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Czech-Polish-Slovak Match
2006 Czech-Polish-Slovak Match
6
6
Part of
2006 Czech-Polish-Slovak Match
Problems
(1)
Pentagon whose diagonal intersections are collinear
Source: Czech-Polish-Slovak 2006 Q6
4/27/2013
Find out if there is a convex pentagon
A
1
A
2
A
3
A
4
A
5
A_1A_2A_3A_4A_5
A
1
A
2
A
3
A
4
A
5
such that, for each
i
=
1
,
…
,
5
i = 1, \dots , 5
i
=
1
,
…
,
5
, the lines
A
i
A
i
+
3
A_iA_{i+3}
A
i
A
i
+
3
and
A
i
+
1
A
i
+
2
A_{i+1}A_{i+2}
A
i
+
1
A
i
+
2
intersect at a point
B
i
B_i
B
i
and the points
B
1
,
B
2
,
B
3
,
B
4
,
B
5
B_1,B_2,B_3,B_4,B_5
B
1
,
B
2
,
B
3
,
B
4
,
B
5
are collinear. (Here
A
i
+
5
=
A
i
A_{i+5} = A_i
A
i
+
5
=
A
i
.)
geometry unsolved
geometry