Geometry · Circle and chord · Reflection · Polygonal chains · Triangle inequality · Half planes
A circle \(k\) has radius \(31\,\mathrm{mm}\), and \(\ell\) is a broken line of length \(61\,\mathrm{mm}\) whose two endpoints both lie on \(k\). Prove that there is a line \(p\) passing through the centre of \(k\) such that every point of \(\ell\) lies on one and the same side of \(p\).
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Serbian Republic Competition (Republicko takmicenje) 2001, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source