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.

Guest Jul 5, 2020

#1**0 **

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).

Guest Jul 5, 2020

#2**0 **

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 ( ON^{2} + NR^{2} ) = 8.062257749

Guest Jul 5, 2020

edited by
Guest
Jul 5, 2020