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 = 12, and PR = 14, then find OR.
QN = 12 PR = 14 PN = 7
F is a foot of the altitude from M to PN
Find angle QPN using QN and PN
Find QP and MP using the Pythagorean theorem
Find MF and PF using angle QPN and MP
Find angle MRF using MF and FR
And finally, find OR = 5*sqrt(2).
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 = 12, and PR = 14, then find OR.
The ratio of ON to QO is 1/2 or 1 : 2
If QN = 12 then ON = 4
If PR = 14 then NR = 7
We have the right triangle ONR
OR = sqrt ( ON2 + NR2 ) = 8.062257749 
