An easy way to a theorem of Kira Adaricheva and Madina Bolat on convexity and circles

Gábor Czédli

paper

An easy way to a theorem of Kira Adaricheva and Madina Bolat on convexity and circles

arXiv:1610.02540

Abstract

Kira Adaricheva and Madina Bolat have recently proved that if $U_{0}$ and $U_{1}$ are circles in a triangle with vertices $A_{0}, A_{1}, A_{2}$ , then there exist $j \in {0, 1, 2}$ and $k \in {0, 1}$ such that $U_{1 - k}$ is included in the convex hull of $U_{k} \cup ({A_{0}, A_{1}, A_{2}} ∖ {A_{j}})$ . We give a short new proof for this result, and we point out that a straightforward generalizaton for shperes fails.

arXiv comment9 pages, 6 figures