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Question Number 173216 by Shrinava last updated on 08/Jul/22

$$\mathrm{O}-\mathrm{circumcenter},\mathrm{I}-\mathrm{incenter},\mathrm{R}-\mathrm{circumradii},$$$$\mathrm{r}-\mathrm{radii},\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}-\mathrm{sides}\mathrm{in}\mathrm{a}\mathrm{bicenteric}$$$$\mathrm{quadrilateral}.\mathrm{Prove}\mathrm{that}:$$$${20\mathrm{I}}^2+\mathrm{r}\sum _{\mathbf{cyc}}\sqrt{{4\mathrm{R}}^2-{\mathrm{a}}^2}=2({\mathrm{R}}^2+{2\mathrm{r}}^2)$$

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