68. In a tetrahedron, three dihedral angles are right angles. One of the segments connecting the midpoints of opposite edges of the tetrahedron is equal to \(a\), and the other is \(b (b > a)\). Find the length of the greatest edge of the tetrahedron.
68. Three right angles cannot adjoin one face; furthermore, they cannot adjoin one vertex, since in this case all segments connecting the midpoints of opposite edges would be equal. The remaining case is when the three edges corresponding to the right angles form an open broken line. Let these be the edges $A B, B C$, and $C D$.

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Fig. 4. Let $|A B|=x, \quad|B C|=y, \quad|C D|=z$. Then the distance between the midpoints of $A B$ and $C D$ will be $\sqrt{\frac{x^{2}}{4}+y^{2}+\frac{z^{2}}{4}}$, and between $A C$ and $B D$ (or $A D$ and $B C$) $-\frac{1}{2} \sqrt{x^{2}+z^{2}}$. The largest will be the edge $\therefore A D \left\lvert\,=\sqrt{x^{2}+y^{2}+z^{2}}=\sqrt{\frac{2}{b^{2}+3 a^{2}} .}\right.$