firstly, I'd like to point out the graph is misleading, if AC is 10 it should be the shorter sides, but it shows as the longer side there.
let's bear in mind that in a rhombus, all sides are equal, even though they may be slanted, the diagonals meet at right-angles always, so the center is simply four 90° angles, and the diagonals bisect each other, namely they cut each other in equal halves.
check the picture below.