The figure shows a quadrilateral ABCD with
AC = CD and angle ACB = angle ACD = 45 degrees. Points
F and E are on CD so that AE is parallel to BC, AB = BE and BE = 2CF. Prove
that BD = 2BF = 3BC.
This entry contributed by Sumith Peiris, Moratuwa, Sri Lanka.
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Original problem 1324.