Mark Shattuck,

A Geometric Inequality for Cyclic Quadrilaterals,

Forum Geometricorum, 18 (2018) 141154.

 

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.

 

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