MathDB

4

Part of 1964 Spain Mathematical Olympiad

Problems(1)

Maximizing a length

Source: http://www.olimpiadamatematica.es/platea.pntic.mec.es/_csanchez/olimp_1963-2004/OME2004.pdf

11/14/2016
We are given an equilateral triangle ABCABC, of side aa, inside its circumscribed circle. We consider the smallest of the two portions of circle limited between ABAB and the circumference. If we consider parallel lines to BCBC, some of them cut the portion of circle in a segment. Which is the maximum possible length for one of the segments?
geometry