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integer ABCD, AB=AD, BC=CD, <ABC=<BCD=<CDA 2020 BMT Team 20

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January 7, 2022
geometryequal segmentsequal angles

Problem Statement

Non-degenerate quadrilateral ABCDABCD with AB=ADAB = AD and BC=CDBC = CD has integer side lengths, and ∠ABC=∠BCD=∠CDA\angle ABC = \angle BCD = \angle CDA. If AB=3AB = 3 and B≠DB \ne D, how many possible lengths are there for BCBC?
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