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A348143
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Areas of integer-sided cyclic quadrilaterals whose area equals their perimeter.
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0
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OFFSET
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1,1
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COMMENTS
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There are no further terms. Note that without the condition "integer-sided" there are other solutions, such as (1, 17/2, 17/2, 16) which has perimeter and area 34.
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LINKS
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EXAMPLE
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The areas or perimeters 16, 18, 20, 30 pertain respectively to cyclic quadrilaterals with sides (4, 4, 4, 4), (3, 3, 6, 6), (2, 5, 5, 8), (5, 5, 6, 14).
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MATHEMATICA
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lst={}; Do[s=(a+b+c+d)/2; If[s>a, (K=Sqrt[(s-a)(s-b)(s-c)(s-d)]; If[IntegerQ[K]&&K==2s, AppendTo[lst, Sort@{a, b, c, d}]])], {a, 1, 15}, {b, 1, a}, {c, 1, b}, {d, 1, c}]; lst
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CROSSREFS
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KEYWORD
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fini,full,nonn
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AUTHOR
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STATUS
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approved
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