Some characterizations of the disc by properties of isoptic triangles

The main result in this article is the following: Let K ⊂ R 2 be a regular convex body and let α , β , θ , be three angles such that K has α -chords, β -chords, and θ -chords of constant length and α + β + θ = π , then K is a disc. We also prove another characterization of the disc with respect to properties of its ( α , β , θ ) -circumscribed triangles.