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(ON2 + NR2) = sqrt(42 + 72)
OR = √85
OR = sqrt(ON2 + NR2) = sqrt(62 + 72)