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Summary

DescriptionCarlitz identity.svg	English: carlitz identity illustration : $\displaystyle x^{2}=R^{2}-2Rr\cdot \mu$ with $\mu$ defined as follows: $\displaystyle {\begin{aligned}\mu &={\sqrt {\frac {(ab+cd)(ad+bc)}{(a+c)^{2}(ac+bd)}}}={\sqrt {\frac {(ab+cd)(ad+bc)}{(b+d)^{2}(ac+bd)}}}\\&={\frac {\cos({\tfrac {\alpha +\gamma }{4}})}{\cos({\tfrac {\alpha -\gamma }{4}})}}={\frac {\cos({\tfrac {\beta +\delta }{4}})}{\cos({\tfrac {\beta -\delta }{4}})}}\end{aligned}}$
Date	5 February 2017
Source	Own work
Author	Kmhkmh

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