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Let the incenters, inradii of four triangles $BCD$, $ACD$, $ABD$, $ABC$ be ($P$,$p$), ($Q$,$q$), ($X$,$x$), ($Y$,$y$) It's known that $\square PQXY$ is rectangle and apply Euler formula to four triangles. $OP^{2}=R^{2}-2Rp$ , $OQ^{2}=R^{2}-2Rq$ , $OX^{2}=R^{2}-2Rx$ , $OY^{2}=R^{2}-2Ry$ In addition, using $~$ $OP^{2}+OX^{2}=OQ^{2}+OY^{2}$ , because $\square PQXY$ is rectangle , we can get it easily.