MathDB

Let

A_1A_2A_3A_4A_5

be a convex 5-gon in which the coordinates of all of it's vertices are rational. For each

1\leq i \leq 5

define

B_i

the intersection of lines

A_{i+1}A_{i+2}

and

A_{i+3}A_{i+4}

. (

A_i=A_{i+5}

) Prove that at most 3 lines from the lines

A_iB_i

(

1\leq i \leq 5

) are concurrent.
Time allowed for this problem was 75 minutes.

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