Final answer:
In a rhombus, the diagonals are perpendicular bisectors of each other, which means they intersect at a 90-degree angle and divide each other into equal halves.
Step-by-step explanation:
A rhombus is inscribed in a circle. The length of one diagonal of the rhombus is 8x. To find the length of the other diagonal, we can use the properties of a rhombus. In a rhombus, the diagonals are perpendicular bisectors of each other, which means they intersect at a 90-degree angle and divide each other into equal halves. Therefore, if one diagonal is 8x, the other diagonal will also be 8x.