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broken link fixed, cf. https://meta.mathoverflow.net/q/5301/70594
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Glorfindel
Glorfindel
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This 1988 paperThis 1988 paper of Innami gives a construction of a convex curve, all of whose points are vertices of billiard triangles and therefore also maximal-perimeter inscribed triangles. In Innami's construction, all triangles are isosceles.

This 1988 paper of Innami gives a construction of a convex curve, all of whose points are vertices of billiard triangles and therefore also maximal-perimeter inscribed triangles. In Innami's construction, all triangles are isosceles.

This 1988 paper of Innami gives a construction of a convex curve, all of whose points are vertices of billiard triangles and therefore also maximal-perimeter inscribed triangles. In Innami's construction, all triangles are isosceles.

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Yoav Kallus
Yoav Kallus
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This 1988 paper of Innami gives a construction of a convex curve, all of whose points are vertices of billiard triangles and therefore also maximal-perimeter inscribed triangles. In Innami's construction, all triangles are isosceles.