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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.

 

 Jul 5, 2020
 #1
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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).

 Jul 5, 2020
 #2
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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   smiley

 Jul 5, 2020
edited by Guest  Jul 5, 2020
 #3
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tysm

Guest Jul 7, 2020

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