Question 6
In convex quadrilateral $KLMN,$ side $\overline{MN}$ is perpendicular to diagonal $\overline{KM},$ side $\overline{KL}$ is perpendicular to diagonal $\overline{LN},$ $MN = 65,$ and $KL = 28.$ The line through $L$ perpendicular to side $\overline{KN}$ intersects diagonal $\overline{KM}$ at $O$ with $KO = 8.$ Find $MO.$