Inegalitate in patrulater inscriptibil

[opincariumihai]

Aratati ca in orice patrulater inscriptibil are loc inegalitatea \( \frac{a+b+c+d}{4}\geq\sqrt{\frac{2\sqrt{2}SR}{p}}\geq \sqrt[4]{abcd}. \)

Mihai Opincariu

[Marius Mainea]

Se folosesc relatiile :

\( S=\sqrt{(p-a)(p-b)(p-c)(p-d)} \)

si

\( R=\sqrt{\frac{(ab+cd)(ac+bd)(ad+bc)}{16(p-a)(p-b)(p-c)(p-d)}} \)