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Pentagon whose diagonal intersections are collinear

Source: Czech-Polish-Slovak 2006 Q6

April 27, 2013

geometry unsolvedgeometry

Problem Statement

Find out if there is a convex pentagon

A_1A_2A_3A_4A_5

such that, for each

i = 1, \dots , 5

, the lines

A_iA_{i+3}

and

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

intersect at a point

B_i

and the points

B_1,B_2,B_3,B_4,B_5

are collinear. (Here

A_{i+5} = A_i