M is the midpoint of PQ and N is the midpoint of PR, and O is the intersection of QN and RM, as shown. If QN is perpendicular to PR, QN = 18, and PR = 14, then find OR.

By the median theorem ON = QN * 1/3 = 6

NR = PR / 2 = 7

OR = sqrt(ON^{2} + NR^{2}) = sqrt(4^{2} + 7^{2})

OR = √85

Corrections:

OR = sqrt(ON2 + NR2) = sqrt(6^{2} + 7^{2})