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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 = 10, and PR = \(15\), then find OR.

 

 Jan 20, 2022
 #1
avatar+189 
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Well, first, triangleMOQ is the same as triangleNOR. We can use this similarity to say QO = RO. Aksi we know PR=15, and since N bisects PR, NR=7.5. We can write an equation which states OR^2=(7.5)^2+ON^2. Also, QO+ON=10 so RO+ON=10. Now that we know this, RO has to be more than 7.5 but less than 8.25. Try solving using that and you will have to do a bit more work.

 Jan 20, 2022
 #3
avatar+1696 
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Sorry to say, but you made a couple of mistakes:

 

1/      Triangles MOQ and NOR are not similar!!!

 

2/      QO and RO are not equal!!! 

civonamzuk  Jan 20, 2022
 #2
avatar+1696 
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QN and RM are the medians of triangle PQR.

 

The ratio of QO to NO is 2:1

 

OR = sqrt[(QN/3)2 + (PR/2)2]

 Jan 20, 2022

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