84. The common chord of two intersecting circles is seen from their centers at angles of $90^{\circ}$ and $60^{\circ}$. Find the radii of the circles if the distance between their centers is $a$.
84. There are two possible cases: both centers are located on opposite sides of the common chord, or on the same side. Accordingly, there are two pairs of answers: $a(\sqrt{3}+1), a \frac{\sqrt{2}}{2}(\sqrt{3}+1)$ and $a(\sqrt{3}-1), a \frac{\sqrt{2}}{2}(\sqrt{3}-1)$.