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AM = CN = a =? if B,M, N are collinear, regular hexagon

Source: 2011 All-Ukrainain Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p9

April 26, 2021

geometryhexagoncollinearequal segmentsUkraine Correspondence

Problem Statement

On the diagonals

AC

and

CE

of a regular hexagon

ABCDEF

with side

1

we mark points

M

and

N

such that

AM = CN = a

. Find

a

if the points

B, M, N

lie on the same line.