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2024 SSMO Team Round Problems/Problem 10

Revision as of 15:44, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== The side-lengths of a convex cyclic quadrilateral <math>ABCD</math> are integers and <math>(AB\cdot AD+BC\cdot CD)^2=AC^2\cdot BD^2-72</math>. Find all possible v...")
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Problem

The side-lengths of a convex cyclic quadrilateral $ABCD$ are integers and $(AB\cdot AD+BC\cdot CD)^2=AC^2\cdot BD^2-72$. Find all possible values of the perimeter of $ABCD$.

Solution

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