Mark Shattuck,
A Geometric Inequality for Cyclic
Quadrilaterals,
Forum Geometricorum,
18 (2018) 141—154.
Abstract.
In this paper, we establish an inequality involving the cosines of the arc
measures determined by four arbitrary points along the circumference of a
circle. Our proof is analytic in nature
and as a consequence of it, we obtain some
inequalities involving the interior angle measures of a triangle. Extending our
arguments yields a sharpened version of the aforementioned
inequality and also the best possible positive constant for which it
holds.